diff --git a/examples/zipf.ipynb b/examples/zipf.ipynb
index 9a3d3683..f7acab96 100644
--- a/examples/zipf.ipynb
+++ b/examples/zipf.ipynb
@@ -23,16 +23,16 @@
     "\n",
     "* Also, what's a chartist?\n",
     "\n",
-    "To answer the second question first, it's someone who supported chartism, which was \"a working-class movement for political reform in the United Kingdom that erupted from 1838 to 1857\", quoth [Wikipedia](https://en.wikipedia.org/wiki/Chartism).  The name comes from the People's Charter of 1838, which called for voting rights for unpropertied men.\n",
+    "To answer the second question first, it's someone who supported chartism, which was \"a working-class movement for political reform in the United Kingdom that erupted from 1838 to 1857\", quoth [Wikipedia](https://en.wikipedia.org/wiki/Chartism).  The name comes from the People's Charter of 1838, which called for voting rights for unpropertied men, among other reforms.\n",
     "\n",
     "To answer the first question, we'll do some Bayesian statistics.\n",
-    "My solution is based on a model that's not very realistic, so we should not take the result too seriously.\n",
-    "But it demonstrates some interesting methods, I think -- and as you'll see, there is a connection to Zipf's law, [which I wrote about last week](https://www.allendowney.com/blog/2024/11/10/zipfs-law/)."
+    "My solution is based on a model that's not very realistic, so we should not take the result too seriously, but it demonstrates some interesting methods, I think.\n",
+    "And as you'll see, there is a connection to Zipf's law, [which I wrote about last week](https://www.allendowney.com/blog/2024/11/10/zipfs-law/)."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 251,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -40,7 +40,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 251;\n",
+       "                var nbb_cell_id = 1;\n",
        "                var nbb_unformatted_code = \"%load_ext nb_black\";\n",
        "                var nbb_formatted_code = \"%load_ext nb_black\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 252,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -77,7 +77,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 252;\n",
+       "                var nbb_cell_id = 2;\n",
        "                var nbb_unformatted_code = \"try:\\n    import empiricaldist\\nexcept ImportError:\\n    !pip install empiricaldist\";\n",
        "                var nbb_formatted_code = \"try:\\n    import empiricaldist\\nexcept ImportError:\\n    !pip install empiricaldist\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -109,7 +109,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 253,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -117,8 +117,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 253;\n",
-       "                var nbb_unformatted_code = \"# download thinkdsp.py\\n\\nfrom os.path import basename, exists\\n\\ndef download(url):\\n    filename = basename(url)\\n    if not exists(filename):\\n        from urllib.request import urlretrieve\\n        local, _ = urlretrieve(url, filename)\\n        print('Downloaded ' + local)\\n        \\ndownload(\\\"https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py\\\")\";\n",
+       "                var nbb_cell_id = 3;\n",
+       "                var nbb_unformatted_code = \"# download thinkdsp.py\\n\\nfrom os.path import basename, exists\\n\\n\\ndef download(url):\\n    filename = basename(url)\\n    if not exists(filename):\\n        from urllib.request import urlretrieve\\n\\n        local, _ = urlretrieve(url, filename)\\n        print(\\\"Downloaded \\\" + local)\\n\\n\\ndownload(\\\"https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py\\\")\";\n",
        "                var nbb_formatted_code = \"# download thinkdsp.py\\n\\nfrom os.path import basename, exists\\n\\n\\ndef download(url):\\n    filename = basename(url)\\n    if not exists(filename):\\n        from urllib.request import urlretrieve\\n\\n        local, _ = urlretrieve(url, filename)\\n        print(\\\"Downloaded \\\" + local)\\n\\n\\ndownload(\\\"https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py\\\")\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 254,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -168,8 +168,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 254;\n",
-       "                var nbb_unformatted_code = \"import numpy as np\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\\n\\nfrom empiricaldist import Pmf\\nfrom utils import decorate\\n\\nplt.rcParams['figure.dpi'] = 75\\nplt.rcParams['figure.figsize'] = [6, 3.5]\";\n",
+       "                var nbb_cell_id = 4;\n",
+       "                var nbb_unformatted_code = \"import numpy as np\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\\n\\nfrom empiricaldist import Pmf\\nfrom utils import decorate\\n\\nplt.rcParams[\\\"figure.dpi\\\"] = 75\\nplt.rcParams[\\\"figure.figsize\\\"] = [6, 3.5]\";\n",
        "                var nbb_formatted_code = \"import numpy as np\\nimport pandas as pd\\nimport matplotlib.pyplot as plt\\n\\nfrom empiricaldist import Pmf\\nfrom utils import decorate\\n\\nplt.rcParams[\\\"figure.dpi\\\"] = 75\\nplt.rcParams[\\\"figure.figsize\\\"] = [6, 3.5]\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 255,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -228,8 +228,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 255;\n",
-       "                var nbb_unformatted_code = \"download('https://www.corpusdata.org/coca/samples/coca-samples-text.zip')\";\n",
+       "                var nbb_cell_id = 5;\n",
+       "                var nbb_unformatted_code = \"download(\\\"https://www.corpusdata.org/coca/samples/coca-samples-text.zip\\\")\";\n",
        "                var nbb_formatted_code = \"download(\\\"https://www.corpusdata.org/coca/samples/coca-samples-text.zip\\\")\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -257,7 +257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 256,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -265,8 +265,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 256;\n",
-       "                var nbb_unformatted_code = \"import zipfile\\n\\ndef generate_lines(zip_path='coca-samples-text.zip'):\\n    with zipfile.ZipFile(zip_path, 'r') as zip_file:\\n        file_list = zip_file.namelist()\\n        for file_name in file_list:\\n            with zip_file.open(file_name) as file:\\n                lines = file.readlines()\\n                for line in lines:\\n                    yield(line.decode('utf-8'))\";\n",
+       "                var nbb_cell_id = 6;\n",
+       "                var nbb_unformatted_code = \"import zipfile\\n\\n\\ndef generate_lines(zip_path=\\\"coca-samples-text.zip\\\"):\\n    with zipfile.ZipFile(zip_path, \\\"r\\\") as zip_file:\\n        file_list = zip_file.namelist()\\n        for file_name in file_list:\\n            with zip_file.open(file_name) as file:\\n                lines = file.readlines()\\n                for line in lines:\\n                    yield (line.decode(\\\"utf-8\\\"))\";\n",
        "                var nbb_formatted_code = \"import zipfile\\n\\n\\ndef generate_lines(zip_path=\\\"coca-samples-text.zip\\\"):\\n    with zipfile.ZipFile(zip_path, \\\"r\\\") as zip_file:\\n        file_list = zip_file.namelist()\\n        for file_name in file_list:\\n            with zip_file.open(file_name) as file:\\n                lines = file.readlines()\\n                for line in lines:\\n                    yield (line.decode(\\\"utf-8\\\"))\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -311,7 +311,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 257,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -319,7 +319,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 257;\n",
+       "                var nbb_cell_id = 7;\n",
        "                var nbb_unformatted_code = \"import re\\nfrom collections import Counter\\n\\ncounter = Counter()\\n\\npattern = r\\\"[ /\\\\n]+|--\\\"\\n\\nfor line in generate_lines():\\n    words = re.split(pattern, line)[1:]\\n    counter.update(word.lower() for word in words if word)\";\n",
        "                var nbb_formatted_code = \"import re\\nfrom collections import Counter\\n\\ncounter = Counter()\\n\\npattern = r\\\"[ /\\\\n]+|--\\\"\\n\\nfor line in generate_lines():\\n    words = re.split(pattern, line)[1:]\\n    counter.update(word.lower() for word in words if word)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -359,12 +359,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The dataset includes more than 190,000 unique strings, but not all of them are what we would consider words."
+    "The dataset includes about 188,000 unique strings, but not all of them are what we would consider words."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 258,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -373,7 +373,7 @@
        "(188086, 11503819)"
       ]
      },
-     "execution_count": 258,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -382,7 +382,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 258;\n",
+       "                var nbb_cell_id = 8;\n",
        "                var nbb_unformatted_code = \"num_words = counter.total()\\nlen(counter), num_words\";\n",
        "                var nbb_formatted_code = \"num_words = counter.total()\\nlen(counter), num_words\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -419,7 +419,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 259,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -427,7 +427,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 259;\n",
+       "                var nbb_cell_id = 9;\n",
        "                var nbb_unformatted_code = \"for s in list(counter.keys()):\\n    if not s[0].isalpha() or not s[-1].isalpha():\\n        del counter[s]\";\n",
        "                var nbb_formatted_code = \"for s in list(counter.keys()):\\n    if not s[0].isalpha() or not s[-1].isalpha():\\n        del counter[s]\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -460,12 +460,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This filter reduces the number of unique words to about 154,000."
+    "This filter reduces the number of unique words to about 151,000."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 260,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -474,7 +474,7 @@
        "(151414, 8889694)"
       ]
      },
-     "execution_count": 260,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -483,7 +483,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 260;\n",
+       "                var nbb_cell_id = 10;\n",
        "                var nbb_unformatted_code = \"num_words = counter.total()\\nlen(counter), num_words\";\n",
        "                var nbb_formatted_code = \"num_words = counter.total()\\nlen(counter), num_words\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -520,7 +520,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 261,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -548,7 +548,7 @@
        " ('we', 47694)]"
       ]
      },
-     "execution_count": 261,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -557,7 +557,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 261;\n",
+       "                var nbb_cell_id = 11;\n",
        "                var nbb_unformatted_code = \"counter.most_common(20)\";\n",
        "                var nbb_formatted_code = \"counter.most_common(20)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -593,7 +593,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 322,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -602,7 +602,7 @@
        "(72159, 0.811715228893143)"
       ]
      },
-     "execution_count": 322,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -611,7 +611,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 322;\n",
+       "                var nbb_cell_id = 12;\n",
        "                var nbb_unformatted_code = \"singletons = [word for (word, freq) in counter.items() if freq == 1]\\nlen(singletons), len(singletons) / counter.total() * 100\";\n",
        "                var nbb_formatted_code = \"singletons = [word for (word, freq) in counter.items() if freq == 1]\\nlen(singletons), len(singletons) / counter.total() * 100\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -648,37 +648,39 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 263,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array(['perfact', 'feidhauses', 'laven', 'osmany', 'nnessee', 'baccardi',\n",
-       "       'eventuate', 'pagando', 'capsulate', 'r-miami', 'soyrizo',\n",
-       "       'narcotic-analgesic', 'phanar', 'midwater', 'chalker', 'fittv',\n",
-       "       'diplomatie', 'queso-broccoli', 'session-and', 'caricaturistes',\n",
-       "       'reverand', 'mesdames', 'flender', 'synchronistic', 'boom-era',\n",
-       "       'litvak', 'skowhegan', 'wailers', 'ambroeus', 'treximet', 'jonell',\n",
-       "       'soundwriters', 'pre-oiled', 'brimless', 'meta-billboard',\n",
-       "       'leather-strapped', 'ludvigsen', 'half-indian', 'bandmembers',\n",
-       "       'pinky-ness', 'pro-marriage-equality', 'bbed', 'sgarlatti',\n",
-       "       'flash-free', 'satelitte', 'goheen', 'med-school', 'lune',\n",
-       "       'remuddled', 'work-rule', 'seawolf', 'instuments', 'gaudiest',\n",
-       "       \"they'lltell\", 'bahrainis', 'deacetylation', 'birth-and-being',\n",
-       "       'captionrodeo', 'cropper', 'dry-mounting', 'marijuana-related',\n",
-       "       'sidelining', 'forexpros', 'aisa', 'naxos', 'g6pd', 'extirpation',\n",
-       "       'colonising', 'faux-relationship', 'peditrician', 'fanboyism',\n",
-       "       'fartlek', 'deacetylation', 'shityou', 'undeservedly', 'budman',\n",
-       "       'upheaving', 'al-fatwa', 'orange-toothed', 'lehy',\n",
-       "       'psychodynamically', 'toys-toys', 'unreason', 'mattatuck',\n",
-       "       'decalogue', 'ritcheychrtien', 'silents', 'scythes', 'bothsighing',\n",
-       "       'dabbler', 'cyclicals', 'mussed', 'odour', 'skandalakis',\n",
-       "       'rayograph', 'boastfulness', 'electro-optical', 'loogierules',\n",
-       "       'wows', 'kornberg'], dtype='<U24')"
-      ]
-     },
-     "execution_count": 263,
+       "array(['leakylibrary', 'vegans-people', 'aurelle', 'dispelling', 'abijah',\n",
+       "       'nation-wide', 'zenker', 'dwigmore.com', 'snake-charmers',\n",
+       "       'andorganization', 'religion-are', 'www.indulgedecor.com',\n",
+       "       'self-enchantment', 're-asserted', 'subvertive', 'guzzles',\n",
+       "       'pdp-4270hd', 'interrogatory', 'peregoy', \"everything'sback\",\n",
+       "       'celexa', 'ychou', \"qu'a\", 'up.according', 'emission-reduction',\n",
+       "       'needthese', 'smker', 'dry-salt', 'kouhei-kun', 'mtv-hyped',\n",
+       "       'downspout', 'favelas', 'machinists', 'non-aspirin',\n",
+       "       'counter-heteronormative', 'mordoh', 'roulon', 'treecovered',\n",
+       "       'alabamians', 'blems', 'collusive', 'concensus', 'unenjoyable',\n",
+       "       'restrictiveness', 'flugsicherung', 'timberline', 'yoo-suk',\n",
+       "       'tania', 'yedu', 'panter', 'dramatica', 'praddock',\n",
+       "       'goldman-fergusons', 'snootful', 'diesel-electric', 'commerice',\n",
+       "       'progrssive', 'maltreating', 'white-clapboard', 'agricutural',\n",
+       "       'then-popular', \"sorry-i'm-late\", 'gamble-all', 'squeamishness',\n",
+       "       'edisons', 'meatside', 'alto-based', 'engine-tuning', 'folk-music',\n",
+       "       'x-i', 'hickam', 'octavius', 'participacin', 'perceivedness',\n",
+       "       'everywhere-and', 'switchblades', 'bocks', 'carbohydr', 'padfield',\n",
+       "       'ctb', 'expropriate', 'yeton', 'hualapai', 'unsinkable',\n",
+       "       'out-island', 'dallal', 'prostate-specific', 'paramecium',\n",
+       "       'one-to-nothing', 'irishamerican', 'zhezha', 'people.theyre',\n",
+       "       'dunphy', 'reclassify', 'southwind', 'roarsandscreeches',\n",
+       "       'dove-gray', 'lololol', 'www.votersfirstohio.com', 'bastide'],\n",
+       "      dtype='<U24')"
+      ]
+     },
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -687,7 +689,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 263;\n",
+       "                var nbb_cell_id = 13;\n",
        "                var nbb_unformatted_code = \"np.random.choice(singletons, 100)\";\n",
        "                var nbb_formatted_code = \"np.random.choice(singletons, 100)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -732,7 +734,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 331,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -740,9 +742,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 331;\n",
-       "                var nbb_unformatted_code = \"freqs = sorted(counter.values(), reverse=True)\";\n",
-       "                var nbb_formatted_code = \"freqs = sorted(counter.values(), reverse=True)\";\n",
+       "                var nbb_cell_id = 14;\n",
+       "                var nbb_unformatted_code = \"freqs = np.array(sorted(counter.values(), reverse=True))\";\n",
+       "                var nbb_formatted_code = \"freqs = np.array(sorted(counter.values(), reverse=True))\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -764,12 +766,12 @@
     }
    ],
    "source": [
-    "freqs = sorted(counter.values(), reverse=True)"
+    "freqs = np.array(sorted(counter.values(), reverse=True))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 332,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -777,7 +779,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 332;\n",
+       "                var nbb_cell_id = 15;\n",
        "                var nbb_unformatted_code = \"n = len(freqs)\\nranks = range(1, n + 1)\";\n",
        "                var nbb_formatted_code = \"n = len(freqs)\\nranks = range(1, n + 1)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -814,7 +816,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 333,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -832,7 +834,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 333;\n",
+       "                var nbb_cell_id = 16;\n",
        "                var nbb_unformatted_code = \"plt.plot(ranks, freqs)\\n\\ndecorate(\\n    title=\\\"Zipf plot\\\", xlabel=\\\"Rank\\\", ylabel=\\\"Frequency\\\", xscale=\\\"log\\\", yscale=\\\"log\\\"\\n)\";\n",
        "                var nbb_formatted_code = \"plt.plot(ranks, freqs)\\n\\ndecorate(\\n    title=\\\"Zipf plot\\\", xlabel=\\\"Rank\\\", ylabel=\\\"Frequency\\\", xscale=\\\"log\\\", yscale=\\\"log\\\"\\n)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -873,7 +875,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 334,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
@@ -882,7 +884,7 @@
        "-5.664633515191604"
       ]
      },
-     "execution_count": 334,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -891,7 +893,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 334;\n",
+       "                var nbb_cell_id = 17;\n",
        "                var nbb_unformatted_code = \"rise = np.log10(freqs[-1]) - np.log10(freqs[0])\\nrise\";\n",
        "                var nbb_formatted_code = \"rise = np.log10(freqs[-1]) - np.log10(freqs[0])\\nrise\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -921,7 +923,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 335,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -930,7 +932,7 @@
        "5.180166032638616"
       ]
      },
-     "execution_count": 335,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -939,7 +941,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 335;\n",
+       "                var nbb_cell_id = 18;\n",
        "                var nbb_unformatted_code = \"run = np.log10(ranks[-1]) - np.log10(ranks[0])\\nrun\";\n",
        "                var nbb_formatted_code = \"run = np.log10(ranks[-1]) - np.log10(ranks[0])\\nrun\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -969,7 +971,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 336,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -978,7 +980,7 @@
        "-1.0935235433575892"
       ]
      },
-     "execution_count": 336,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -987,7 +989,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 336;\n",
+       "                var nbb_cell_id = 19;\n",
        "                var nbb_unformatted_code = \"rise / run\";\n",
        "                var nbb_formatted_code = \"rise / run\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1035,7 +1037,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 267,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -1043,7 +1045,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 267;\n",
+       "                var nbb_cell_id = 20;\n",
        "                var nbb_unformatted_code = \"def describe(seq):\\n    return pd.Series(seq).describe()\";\n",
        "                var nbb_formatted_code = \"def describe(seq):\\n    return pd.Series(seq).describe()\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1073,24 +1075,141 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 268,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "data": {
+      "application/javascript": [
+       "\n",
+       "            setTimeout(function() {\n",
+       "                var nbb_cell_id = 21;\n",
+       "                var nbb_unformatted_code = \"num_words = counter.total()\\nrates = np.array(freqs) / num_words\";\n",
+       "                var nbb_formatted_code = \"num_words = counter.total()\\nrates = np.array(freqs) / num_words\";\n",
+       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
+       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
+       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
+       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
+       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
+       "                        }\n",
+       "                        break;\n",
+       "                    }\n",
+       "                }\n",
+       "            }, 500);\n",
+       "            "
+      ],
       "text/plain": [
-       "count    151414.000000\n",
-       "mean          6.604409\n",
-       "std         221.228503\n",
-       "min           0.112490\n",
-       "25%           0.112490\n",
-       "50%           0.224980\n",
-       "75%           0.674939\n",
-       "max       51969.280382\n",
+       "<IPython.core.display.Javascript object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "num_words = counter.total()\n",
+    "rates = np.array(freqs) / num_words"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/javascript": [
+       "\n",
+       "            setTimeout(function() {\n",
+       "                var nbb_cell_id = 70;\n",
+       "                var nbb_unformatted_code = \"from scipy.stats import beta\\n\\nnp.random.seed(17)\\nalphas = freqs + 1\\nbetas = num_words - freqs + 1\\ninferred_rates = beta(alphas, betas).rvs()\";\n",
+       "                var nbb_formatted_code = \"from scipy.stats import beta\\n\\nnp.random.seed(17)\\nalphas = freqs + 1\\nbetas = num_words - freqs + 1\\ninferred_rates = beta(alphas, betas).rvs()\";\n",
+       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
+       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
+       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
+       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
+       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
+       "                        }\n",
+       "                        break;\n",
+       "                    }\n",
+       "                }\n",
+       "            }, 500);\n",
+       "            "
+      ],
+      "text/plain": [
+       "<IPython.core.display.Javascript object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from scipy.stats import beta\n",
+    "\n",
+    "np.random.seed(17)\n",
+    "alphas = freqs + 1\n",
+    "betas = num_words - freqs + 1\n",
+    "inferred_rates = beta(alphas, betas).rvs()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/javascript": [
+       "\n",
+       "            setTimeout(function() {\n",
+       "                var nbb_cell_id = 71;\n",
+       "                var nbb_unformatted_code = \"# rates = np.where(freqs <= 500, inferred_rates, rates)\";\n",
+       "                var nbb_formatted_code = \"# rates = np.where(freqs <= 500, inferred_rates, rates)\";\n",
+       "                var nbb_cells = Jupyter.notebook.get_cells();\n",
+       "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
+       "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
+       "                        if (nbb_cells[i].get_text() == nbb_unformatted_code) {\n",
+       "                             nbb_cells[i].set_text(nbb_formatted_code);\n",
+       "                        }\n",
+       "                        break;\n",
+       "                    }\n",
+       "                }\n",
+       "            }, 500);\n",
+       "            "
+      ],
+      "text/plain": [
+       "<IPython.core.display.Javascript object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# rates = np.where(freqs <= 500, inferred_rates, rates)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "count    1.514140e+05\n",
+       "mean     5.232601e+06\n",
+       "std      1.229446e+07\n",
+       "min      1.922305e+01\n",
+       "25%      1.155947e+06\n",
+       "50%      2.857156e+06\n",
+       "75%      5.699856e+06\n",
+       "max      1.359491e+09\n",
        "dtype: float64"
       ]
      },
-     "execution_count": 268,
+     "execution_count": 72,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -1099,9 +1218,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 268;\n",
-       "                var nbb_unformatted_code = \"n = counter.total()\\nrates = np.array(freqs) / n\\ninverse_rate = 1 / rates\\ndescribe(inverse_rates)\";\n",
-       "                var nbb_formatted_code = \"n = counter.total()\\nrates = np.array(freqs) / n\\ninverse_rate = 1 / rates\\ndescribe(inverse_rates)\";\n",
+       "                var nbb_cell_id = 72;\n",
+       "                var nbb_unformatted_code = \"inverse_rates = 1 / inferred_rates\\ndescribe(inverse_rates)\";\n",
+       "                var nbb_formatted_code = \"inverse_rates = 1 / inferred_rates\\ndescribe(inverse_rates)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -1123,9 +1242,7 @@
     }
    ],
    "source": [
-    "n = counter.total()\n",
-    "rates = np.array(freqs) / n\n",
-    "inverse_rate = 1 / rates\n",
+    "inverse_rates = 1 / inferred_rates\n",
     "describe(inverse_rates)"
    ]
   },
@@ -1138,24 +1255,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 278,
+   "execution_count": 73,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "count    151414.000000\n",
-       "mean          6.341648\n",
-       "std           0.673543\n",
-       "min           1.285082\n",
-       "25%           6.062383\n",
-       "50%           6.456414\n",
-       "75%           6.758455\n",
-       "max           9.275781\n",
+       "mean          6.340519\n",
+       "std           0.672521\n",
+       "min           1.283822\n",
+       "25%           6.062938\n",
+       "50%           6.455934\n",
+       "75%           6.755864\n",
+       "max           9.133376\n",
        "dtype: float64"
       ]
      },
-     "execution_count": 278,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -1164,7 +1281,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 278;\n",
+       "                var nbb_cell_id = 73;\n",
        "                var nbb_unformatted_code = \"mags = np.log10(inverse_rates)\\ndescribe(mags)\";\n",
        "                var nbb_formatted_code = \"mags = np.log10(inverse_rates)\\ndescribe(mags)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1202,7 +1319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 279,
+   "execution_count": 74,
    "metadata": {},
    "outputs": [
     {
@@ -1210,7 +1327,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 279;\n",
+       "                var nbb_cell_id = 74;\n",
        "                var nbb_unformatted_code = \"from empiricaldist import Surv\\n\\n\\ndef make_surv(seq):\\n    \\\"\\\"\\\"Make a non-standard survival function, P(X>=x)\\\"\\\"\\\"\\n    pmf = Pmf.from_seq(seq)\\n    surv = pmf.make_surv() + pmf\\n\\n    # correct for numerical error\\n    surv.iloc[0] = 1\\n    return Surv(surv)\";\n",
        "                var nbb_formatted_code = \"from empiricaldist import Surv\\n\\n\\ndef make_surv(seq):\\n    \\\"\\\"\\\"Make a non-standard survival function, P(X>=x)\\\"\\\"\\\"\\n    pmf = Pmf.from_seq(seq)\\n    surv = pmf.make_surv() + pmf\\n\\n    # correct for numerical error\\n    surv.iloc[0] = 1\\n    return Surv(surv)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1256,17 +1373,69 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 318,
+   "execution_count": 75,
    "metadata": {},
    "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>probs</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>8.961709</th>\n",
+       "      <td>0.000020</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8.992684</th>\n",
+       "      <td>0.000013</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9.133376</th>\n",
+       "      <td>0.000007</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "8.961709    0.000020\n",
+       "8.992684    0.000013\n",
+       "9.133376    0.000007\n",
+       "Name: , dtype: float64"
+      ]
+     },
+     "execution_count": 75,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
     {
      "data": {
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 318;\n",
-       "                var nbb_unformatted_code = \"surv = make_surv(mags)\";\n",
-       "                var nbb_formatted_code = \"surv = make_surv(mags)\";\n",
+       "                var nbb_cell_id = 75;\n",
+       "                var nbb_unformatted_code = \"surv = make_surv(mags)\\nsurv.tail()\";\n",
+       "                var nbb_formatted_code = \"surv = make_surv(mags)\\nsurv.tail()\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -1288,7 +1457,8 @@
     }
    ],
    "source": [
-    "surv = make_surv(mags)"
+    "surv = make_surv(mags)\n",
+    "surv.tail()"
    ]
   },
   {
@@ -1300,12 +1470,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 319,
+   "execution_count": 76,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -1318,7 +1488,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 319;\n",
+       "                var nbb_cell_id = 76;\n",
        "                var nbb_unformatted_code = \"surv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (log10 words per appearance)\\\", ylabel=\\\"Tail probability\\\")\";\n",
        "                var nbb_formatted_code = \"surv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (log10 words per appearance)\\\", ylabel=\\\"Tail probability\\\")\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1357,12 +1527,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 320,
+   "execution_count": 77,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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dZ69Yjtd9lwfsPXNeomrI6qCLjY2FRqOBWq222J+QkAB/f3/06tUL0dHRMBqNtR5nzJgxWLt2LTZv3owdO3Y0rGoiIpk7sni4xfaCjWkSVUJWB92UKVNw/LjlrShMJhOio6Oxbds2nD9/HsXFxYiLiwMApKSkYOzYsRZfSUm/91W/8847mD9/fhO9DSIiefHq6IJZlnNT8Pw6dmFKQSGEEPV5gVqtRmVlJQDg6NGjWLRoERITEwEA+/btg16vx65du2o9xhtvvIHevXtj2rRpdZ7Pz88Pqamp9SmRiEg2ei/Zg1t3bH84qw8e8+stWT32qrasaNQYncFggLe3t3nbx8cHmZmZtb7mP//5Dz777DMkJCTgtddeu+txvV4PPz8/81dhYWFjSiQiktTR/xtpsf30/zuHykqTRNW0Tuq6n1KzejYGAQDz58+vtctSp9NBp9OZt/38/BpUGxGRHHR0bYc/P+KO9/ZeM++LfOW/2FXNncqpeTSqReft7W3RgsvIyIBGo2l0UQAXdSYi+/FMxFA87v/79i8A9AePSFZPa9OooAsNDYXBYDD3i65btw6RkZFNUhgXdSYie7J8pmUL7u//5bBMS7E66GJiYqDRaGA0GqHRaKDT6aBSqbB27VpERUWhZ8+ecHZ2xsyZM5ukMLboiMjefPnsQIvtDw4kSlRJ61LvWZctjbMuicieBLy6B9fvmIb59cLB6NPVQ7qC7ESzzbpsTmzREZE9OrR4lMX2Qyt/lKiS1kO2QccxOiKyR+4ujng9ynLS3tbk0xJV0zrINujYoiMiezUrNMhie/Fn6bhWUiZRNfaPY3RERBJIz7uGiBWHLffx2roGs8kxOiIie+br6Y43p3hb7OMdDpqHbIOOXZdEZO9mDAiE+o6/wgs2piE975pk9dgrdl0SEUnoSuF1DF5+0GIfuzDrj12XREQy1bWDMz75U6DFvkO/ZUhUjX1i0BERSez+e73Rvs3v2zP+k4LcazekK8jOyDboOEZHRK1J4p8fsNgO+1uCNIXYIdkGHS8YJ6LWpJNbe3z+VLDFvgu5XPi5Kcg26IiIWpvQe7wstke+z1v5NAUGHRGRjCS8ONRiOzU7T6JK7Idsg45jdETUGvl6usO9ncq8/dg/j0lYjX2QbdBxjI6IWqtvnx9hsX0qK1eiSuyDbIOOiKi16ujaDsP7uJu3x65KwpXC69IVZOMYdEREMvTv6YOguGN78PKDyC7gUE5DMOiIiGTI0VGNH16y7MK8/91EFBTflKgi28WgIyKSqa4dnPHT/4202Bf69rcSVWO7GHRERDLW0bUdjiwebt42ASi+Xi5dQTZItkHHywuIiKp4dXSBw+9XHGDU8v3SFWODZBt0vLyAiOh3B//8+3hd3i3glZ0nUVFhlLAi2yHboCMiot917eCMb1+437wdd9SA13Yel7Ai28GgIyKyEfd27oBDi4aZtz/5+SpnYVqBQUdEZEM0Hq7w6+ps3g57+1t2YdaBQUdEZGO2zh9i/r4SwBu7fpauGBvAoCMisjHOTm1xbEmEeXvT8Rxcv1EhXUEy1+JB9+uvv2LBggWYO3cuXn755ZY+PRGRXejs7gT/rr/PSp+0+jsJq5E3q4MuNjYWGo0GarXaYn9CQgL8/f3Rq1cvREdHw2isva+4d+/e+Oijj7B+/XqcO3euYVUTERG2zB9s/v7XwkpeSF4Dq4NuypQpOH7cciqryWRCdHQ0tm3bhvPnz6O4uBhxcXEAgJSUFIwdO9biKykpCQDwzTffIDIyEgMHDmzCt0JE1Lo4O7XFrEHe5u2gN/fjalGphBXJk0IIIerzArVajcrKSgDA0aNHsWjRIiQmJgIA9u3bB71ej127dll1rLFjx2Lnzp1o06ZNjc/x8/NDampqfUokImo1KiqM+Nt/T+HjHwwAABWA0689DEdHde0vtDO1ZUWjPgmDwQBv79//m/Dx8UFmZmatrzl8+DC2bNmCW7duITg4+K6Q0+v10Ov15u3CwsLGlEhEZNfatlXhLxOCcCy9CKcul8AIYOFnSfhozpA6X9taNCro6tkYBAAMHToUQ4cOrfFxnU4HnU6H+Ph4xMfH48CBA40pkYioVfgsejAC3vgGAPD12QJcv1EBZ6e2ElclD42adent7W3RgsvIyIBGo2l0UQDXuiQiqg9np7Z45bG+AKrucDDlo++lLUhGGhV0oaGhMBgM5n7RdevWITIyskkK490LiIjqZ87998LNserP+q/5Zby27n+sDrqYmBhoNBoYjUZoNBrodDqoVCqsXbsWUVFR6NmzJ5ydnTFz5swmKYwtOiKi+lGrlVg1LQQAUGkCxq1OhMlU/yEme2P1GN2aNWuq3T9y5MhmmRV5e4yOLToiIuuF9+mMnp7t8VteKS4WluPQhVwM79VF6rIkJdslwNiiIyKqP6VSgS8WDEUbRdX20q2/oLLSJG1REpNt0BERUcM4O7XFIwFdAQBZxRXY+OMFiSuSlmyDjpNRiIga7u+Tg+DqUNWs++i7C636Vj6yDTp2XRIRNZyjoxovjO4HAMi7cQt//jy51U5MkW3QERFR48wY4ovA7q4AgC9/uYIjF/Mkrkgasg06dl0SETWOWq3E1vlD4NKm6iLyD/e3zjvGyDbo2HVJRNR4jo5qBHp3AABcKihrlWN1sg06IiJqGs9E9AYAZBWVY9H21jdWJ9ugY9clEVHTGNSrE8YFVl1u8NWpHBy7lC9xRS1LtkHHrksioqahVCqwIkqL+7o44ZZR4MMDv7aqi8hlG3RERNR02rZV4YlBvgCAxPMF2Jx0SdqCWhCDjoiolZgW5oNQn6rLDU5cLGg1Y3UMOiKiVkKtVmKi1hsAsO906xmrk23QcTIKEVHTmxbmg2G9PVBuFNhyNKNVtOpkG3ScjEJE1PTUaiWejeiNNsrW06qTbdAREVHzCO3REWMCu6H0lqlVtOoYdERErYxSqcD0gffAQaXA/jO5OJ5RIHVJzYpBR0TUCoX26IjHQzUoKTfiTHaR1OU0KwYdEVErpFQq0K6tGgDwc8Y1u+6+lG3QcdYlEVHzevHBvhjeywOJ567adfelbIOOsy6JiJpX27YqBPu4o7D0FtIuF0tdTrORbdAREVHz6+zqCAHgxKVCu13/kkFHRNSKPR7qgxG9O2H3ycvYciJT6nKaBYOOiKgVU6uViLjPEw5tVLi3U3upy2kWDDoiolbOaBS4WWHEhbwbUpfSLBh0REStXJDGHa7t1KgUAt+dzbW7Sw0kCTqj0YjHHnsMK1eulOL0RER0hwH3dMT6uWHw6+qKP287iZ8yC6UuqUlZHXSxsbHQaDRQq9UW+xMSEuDv749evXohOjoaRqOxzmP94x//wPjx4+tfLRERNTmlUoEQnw4AgFtGE0RrbdFNmTIFx48ft9hnMpkQHR2Nbdu24fz58yguLkZcXBwAICUlBWPHjrX4SkpKQlJSEhwdHdGvX7+mfSdERNQoSoUCjm2U+ObMFZxIt58bsyqEEPV6J2q1GpWVlQCAo0ePYtGiRUhMTAQA7Nu3D3q9Hrt27arx9W+99RZyc3ORlZWFvLw8fPLJJ+jevXuNz/fz80Nqamp9SiQiogYwmQS2HM/EP/afQ6VR4KMZIQjr4SF1WVapLSvU1e61ksFggLe3t3nbx8cHmZm1X4fx8ssvA6jq8kxOTr4r5PR6PfR6vXm7sNC++oqJiORKqVTg8VBv9O7iDGESKC6vxE8ZhdBq3KFUKqQur8EaNRmlno1BCxEREVi4cOFd+3U6HVJTU81fHTp0aESFRERUH0qlAqH3dMTAHh6oqDQh5v+dsPnJKY0KOm9vb4sWXEZGBjQaTaOLArioMxGR1Do7O0AIExLP5dn0eF2jgi40NBQGg8HcL7pu3TpERkY2SWFc1JmISFrBPh3w4sP9sDUpExt/SLfZsLM66GJiYqDRaGA0GqHRaKDT6aBSqbB27VpERUWhZ8+ecHZ2xsyZM5ukMLboiIikdXvMLnZ0H6w5eAEJ53LxU0ahzQVevWddtjTOuiQikpbJJJBsuIaTmdew8Ug63n9ca77uTi6abdZlc4qPj0d8fDxbdEREErt9QXlHpzYorzQi0MtN6pLqRbZrXXKMjohIXgquV2DjkUvYdsKA87nXpS7HamzRERGRVbTeHaB/IgRajTuKy24hKb0Al6+VYWxgN1lfZ8cWHRERWeV2F6ZSqYB7+7ZQKRV4+79nkCzz6+xkG3RERCRvWo07/h4ViPT8UlnPxJRt0PHyAiIieVMqFXByUOPv+9KQbLgmdTk1km3QseuSiEj+Ar3cMCm4u6xnYso26IiISP5+yS7Czp+z8Et2kdSl1IhBR0REDabVuOO5Ub0hTEK243SyDTqO0RERyZ9SqYBbOzUWbkmW7TgdlwAjIqJGuX3D1sdDvSW7nq62rJBti46IiGyDUqlA7y7OSDZck2X3JYOOiIga7bfcG3hBpt2XDDoiImq03l2c8f7jWmg17lKXcheudUlERI2mUigQ5O0udRnVkm2LjheMExHZDoc2Shw4k8MxOiIisk+lFUa8Gn8KX6VclrqUuzDoiIio0bQad6x+IgT9NW5IMchrlRQGHRERNdrtW/jc4+GE7h3a4Yff8iGXy7QZdERE1KQ6OrVFyD3uOHguDz9eyJd83E62QcclwIiIbJeDWgVXR3ksDcYlwIiIqFmYTAJbj2diagssDcYlwIiIqMUplQr07eoi2fqX5jokPTsREdm1Du3bovBGhaQ1MOiIiKjZ3OPRHpcKSiWtgUFHRETNRqFQSH6ZAYOOiIiaVaXJhJ8uFUh2mUGLB11CQgKGDh2KBQsWYNu2bS19eiIiamGVRgHdJz9LdpmB1UEXGxsLjUYDtdryhgcJCQnw9/dHr169EB0dDaPRWOtxFAoFnJ2dUVpainvvvbdhVRMRkc0Y1MMDsaN6o18XaRbpt/o6ukOHDqFXr17QaDSorKwEAJhMJvTp0we7du2Cn58fpk6dijFjxmD27NlISUnB0qVLLY6xbNkyDBgwAEqlEjdu3MDUqVOxZ8+eWs/L6+iIiGyfEAJJ6YUI69GxWY5fW1ZYfT+68PDwu/YlJSXBy8sLfn5+AIB58+ZBr9dj9uzZ6N+/P7788ssaj+fk5CT5ACUREbUMhUIBTxcH5JaUobOLY4ueu1E3XjUYDPD29jZv+/j4IDMzs9bX7NixA3v37sX169cxe/bsux7X6/XQ6/Xm7cLCwsaUSEREMtGjkxOOXSywraBrSIssMjISkZGRNT6u0+mg0+nM27dbi0REZPt6dXbGrzkl6N2C43WNCjpvb2+LFlxGRgY0Gk2jiwKqFnWOj4/nos5ERHako1Nb/JZ3HUaTgKqFlgZr1OUFoaGhMBgM5gHAdevW1dpaq4+JEydiw4YNcHGRZpYOERE1D623O5IzW25Yyuqgi4mJgUajgdFohEajgU6ng0qlwtq1axEVFYWePXvC2dkZM2fObJLCeJseIiL71EalRPu2ahTdvNUi5+NteoiISBJHL+Rj0L0eTXIsm7xND1t0RET2rXuHdjhy/mqzLw0m26DjGB0RkX3LLSnH/+1MafalwRo167I5cdYlEZF902rc8f7jWmg17s16Ho7RERGRzbPJMToiIqKmwK5LIiKya+y6JCIim8euSyIiarUYdEREZNc4RkdERHZN9mN0rq6ud90RobCwEB06dJCoooZj3S3HFmsGWHdLs8W6bbFmoPnrNhgMKC4urvYx2QdddWx1ggrrbjm2WDPAuluaLdZtizUD0tbNMToiIrJrDDoiIrJrNhl0Op1O6hIahHW3HFusGWDdLc0W67bFmgFp67bJMToiIiJr2WSLjoiIyFo2FXSxsbHQaDRQq2V7+d9dMjMzMWrUKNx3333w9/fH0qVLpS7Jag899BC0Wi369++PqKioGqfuypVOp7Op3xVfX1/4+/tDq9VCq9UiJSVF6pLqdOPGDcyePRt9+/ZFv379sGbNGqlLqlNubq75M9ZqtejatSsmTZokdVlWiYuLQ2BgILRaLYYNG4a0tDSpS6rTRx99hICAAPj7++Ppp5+G0Whs+SKEDfn+++/F5cuXhUqlkroUq2VnZ4ukpCQhhBDl5eUiPDxcxMfHS1yVda5du2b+PjY2Vixbtky6YuopMTFRzJo1y6Z+V+655x6RmZkpdRn1EhMTI5YvXy6EEMJkMomcnByJK6q/UaNGic2bN0tdRp1u3LghOnbsKPLy8oQQQvzrX/8SUVFREldVu1OnTomePXua/5Y899xzYuPGjS1eh0216MLDw9G1a1epy6iXbt26ITQ0FADQtm1bBAcHIyMjQ+KqrOPm5gYAMJlMKCsrg0KhkLgi65SXl2PJkiV47733pC7FrpWUlGDXrl144YUXAAAKhQKdO3eWuKr6yc7OxvHjxzFx4kSpS6mTyWSCEALXr18HABQVFaFbt24SV1W71NRUDBo0yPy35OGHH8aWLVtavA6bCjpbV1BQgPj4eDz44INSl2K1SZMmoXPnzkhLS8OLL74odTlWef311zFv3jx4enpKXUq9jRs3DlqtFi+//DJu3boldTm1unDhArp06YJnnnkGISEhmDRpEi5duiR1WfXy6aefYuLEiWjfvr3UpdTJ2dkZq1evRkBAALp3746NGzfijTfekLqsWgUGBuLQoUPIzs6G0WjEtm3bkJmZ2eJ1MOhaSEVFBaKiohAbG4t+/fpJXY7Vdu7ciezsbGg0Gnz++edSl1OnX375BUePHsXcuXOlLqXevv/+e/z88884fPgw0tLSZN8iraysRHJyMqKiovDTTz9h3LhxePLJJ6Uuq17i4uIwY8YMqcuwyq1bt/Dhhx8iKSkJWVlZiIqKwksvvSR1WbXq27cv3nrrLYwfPx7h4eHw9vaGSqVq8ToYdC3AaDRi+vTp0Gq1NtMqulPbtm0xbdo07Ny5U+pS6nT48GGkpqaiR48e8PX1hdFohK+vr01MpPH29gYAODk5ITo6GkeOHJG4otppNBp4eHhg9OjRAIBp06bhxIkTEldlvdTUVOTl5WHkyJFSl2KV5ORkCCFw3333Aaj6vOX+OwIAM2bMwPHjx/HDDz8gODhYkn/0GXQt4E9/+hNcXFywYsUKqUuxWklJCS5fvgygamxg165d8Pf3l7iquj311FPIzs5Geno60tPToVKpkJ6eDldXV6lLq9WNGzfMYWw0GrF9+3YEBgZKXFXtunTpAn9/f/z0008AgG+++cYmfkdu27RpE6ZPnw6l0jb+DGo0GqSlpSErKwtA1eft5+cncVV1y8nJAQAUFxdj+fLlePbZZ1u8Bpu6YDwmJgZ79uxBVlYWunfvjgkTJkCv10tdVq0OHz6M8PBwBAQEmJvsTz75JJ577jmJK6tddnY2JkyYgPLycphMJgwaNAirVq2yibGMO6nValRWVkpdRp0uXLiAyMhImEwmGI1GDBkyBP/85z9l/3mnpqZi3rx5uHHjBtzd3bFmzRpzi0POhBDw9fXF7t27Zf8PxZ3Wrl2L999/H23atIGnpyc+/vhj+Pj4SF1WrR544AHk5ORACIFFixZJ0r1tU0FHRERUX7bRZiciImogBh0REdk1Bh0REdk1Bh0REdk1Bh0REdk1Bh0REdk1Bh01mC3dAsca8fHx+OWXXxr02oceesh8IW9zsrfP3BaYTCYMGzYM165dk7oUaiAGHclaU17sXdexGhp0Bw4cQPfu3dG9e/eGllYtqS90l/r8dWmp+pRKJebMmYMPPvigRc5HTY9BR01CrVbj9ddfh1arRWBgIM6dOwchBHr06GHR0hkzZgy+/vprAMCqVasQFhaGoKAgREdHm1fr9/X1xZIlSxAaGopVq1Zh586d5ptNBgYGmlfIT0hIQHh4OAYMGICHHnqo2lXRN2zYgLFjx+Lhhx9GQEAAACAqKgqhoaEICAjA888/DwD47rvvsGvXLrz88svQarU4cuQIbt68iQULFiAsLAz9+/fH6tWrq33vGzduRFRUFICqsLy9oHR8fDzUarV5aa9evXqhqKgIFRUVeOqppxAQEICAgACsXbvW4nN85ZVXEBwcjB07diA5ORnBwcEIDAzEsmXLzM/LycnByJEjodVq4e/vjw8//LDa9z5u3DiMHj0affv2xezZs1FRUQEAuHTpEsaOHYvQ0FCEhobi4MGDNX5ed3r77bcxcOBABAUFYezYscjPz6/zXBEREXj++ecREhKC3r1747PPPjMfb9u2bRg0aBCCg4MxefJkFBUV1Xkea36eADBnzhw888wzCA8PR48ePSxWUfr222/Nv3sDBw5EQUEBgJp/JyMjI7Fp06Zqf/5kA1r8DnhkN+68qSkA8emnnwohhPj73/8uoqOjhRBCvPTSS+K9994TQghx9epVodFoRGVlpThw4ICYMWOGMBqNQgghdDqd+PDDD4UQVTcgffXVV83H7t+/v8jOzhZCCFFaWipu3rwp8vPzxZAhQ8w3dNy6dauYOnXqXTWuX79edOrUSVy5csW87+rVq0IIIYxGo5gwYYLYu3evEEKI2bNni02bNpmf9+qrr4o1a9YIIYQoKysTAwYMEKdPn77rHL6+vubjX716VfTs2VMIIcTChQtFWFiY2LNnj7h48aIYMGCAEEKIlStXismTJwuj0Sjy8/NFjx49xKlTp8yf47p168zHDgwMNNe3cuVK82e+YsUK8fbbb5ufV1BQUO17d3d3FwaDQZhMJhEZGSlWrVolhBBi5MiR5nNeunRJ9OjRQ5hMpmo/rzvd/uxu17BkyZI6zzVixAgxdepUYTKZREZGhujSpYvIyckRZ8+eFQ8++KAoKysTQgjx7rvvisWLF9d5nvr8PMeMGSMqKytFVlaWcHNzExUVFSIvL094eXmJM2fOCCGEKC4uFuXl5bX+TgohRK9evYTBYKj2cyF5Y4c/NQmFQoHJkycDAAYOHIi9e/cCAJ544gnMnj0bL774IrZu3YrIyEioVCp89dVXSExMREhICACgrKwM7dq1Mx/viSeeMH8fERGBGTNmYOLEiZgwYQJ8fHywf/9+pKWlYcSIEQCqxlFcXFyqrW306NHo0qWLefvf//43tm7dCqPRiNzcXISHh+Phhx++63VfffUVbt68aW4tFRcXIy0t7a6FdC9fvmy+952HhwecnJyQmZmJH374AUuXLsXBgweRm5trrjUhIQHR0dFQKpXo2LEjxo8fj4MHD5oXRJ4+fTqAqhtrXr582VzbnDlzzHe/GDRoEObOnYuSkhI88sgjGD58eI3v/XaX6qxZsxAXF4c5c+bg0KFDFp9xRUUFcnNzq/287nTkyBG88847KCkpwc2bNy1Woq/uXM8884x5W6FQwNvbG0OGDEFSUhIuXryIlJQUDBo0CEDVbWj69+9v1Xms/XlOmjQJKpUKXl5e6NChA3JycpCcnIzBgwebj3n796au38nOnTsjOzu7ybuoqfkx6KhJKJVKtGnTBgCgUqnM4yf9+/dHZWUlzp49i08++cR8BwchBJ5//nksXLiw2uM5OTmZv//nP/+Jn3/+Gd988w1GjBiBuLg4CCEwbNgwxMfH11nbncc6ePAgtm/fjsTERLi4uODFF19EWVlZta8TQmDz5s3QarW1Ht/R0RHl5eXmP4ojRozAF198AQcHBzz44INYsWIFcnJyEBkZCQB33an9zm2VSgVHR8c639PQoUNx+PBh7N27F2+99Ra2bNlS7QLn1d0V3mQyoX379khOTq722Hd+XncqLy/HnDlzcOzYMfTs2RO7d++2GLeq7Q701T0mhMDjjz+OlStX1us89fl5Ojg4mL+//Xspaljet67fyT8GH9kOjtFRs5s+fTreeecd5ObmIiwsDADw6KOPYv369eaZbIWFhbh48WK1rz937hyCg4OxePFiPPjgg0hOTsaQIUNw7NgxnDp1CkBVayAlJaXOWoqKiuDu7g4XFxfk5+dj+/bt5sdcXFws7lv36KOP4oMPPoDRaAQA/Prrr9Xe187f3x+//vqreXvEiBF49913MWzYMPMf5QMHDphbXREREdi4cSOEECgsLMTu3bvNrb07ubm5wcvLC9988w0AWIwRpaenw93dHTNnzsSyZctw7Nixat/v/v37cfnyZQghEBcXhxEjRsDV1RX+/v74+OOPzc+7faud2pSVlcFkMqFz584wGo1Yt25dnee6bdOmTRBCICsrCz/++CPCwsIwevRo7Ny5EwaDAQBQWlqKs2fP1nmeO9X286zJkCFD8OOPP+Ls2bMAqm5JVVFRUevvpBACmZmZ6N27d53HJ/lh0FGzmz59OjZt2oRp06aZ940ePRoLFizA8OHDERgYiFGjRpn/4P3R4sWLERAQAK1Wi5ycHMyYMQOdOnXCp59+iujoaAQFBUGr1SIxMbHOWh555BE4Ozujb9++iIqKsujymz59OlavXm2ejPLKK6/A2dkZQUFBCAgIwPz5880TLO40fvx4HDhwwLw9fPhwGAwGREREAKhqfXXq1Anu7u4AgAULFsDDwwP9+/fHsGHDsGTJkhrv47ZhwwYsXrwYgYGBuHr1qnn/d999h+DgYAQHB+PZZ5/F8uXLq3390KFDMXPmTPTr1w/t2rXD/PnzAQCbN2/Gzp07ERQUBD8/vxon2tzJzc0NL7zwAgIDAzF48GD06dPHqnMBQNeuXTFgwAA88MADeP/99+Hp6Yn77rsP77//PsaPH4+goCAMHjwYp0+frvM8d6rt51mTTp06YdOmTZgxYwaCgoIwevRoXL9+vdbfyaSkJAwaNMiihUi2g7fpIWqkvLw8TJgwAYcPH661+66lbdiwAYcOHbKY1SnFuSIiIvDmm28iPDy82etoLjExMZg6dSpGjRoldSnUAGzRETWSp6cnXnrpJVy5ckXqUqgZmEwmhISEMORsGFt0RERk19iiIyIiu8agIyIiu8agIyIiu8agIyIiu8agIyIiu8agIyIiu/b/A+aWmfsN2mujAAAAAElFTkSuQmCC",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -1375,7 +1545,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 320;\n",
+       "                var nbb_cell_id = 77;\n",
        "                var nbb_unformatted_code = \"surv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (words per appearance)\\\", yscale=\\\"log\\\")\";\n",
        "                var nbb_formatted_code = \"surv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (words per appearance)\\\", yscale=\\\"log\\\")\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1427,7 +1597,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 291,
+   "execution_count": 78,
    "metadata": {},
    "outputs": [
     {
@@ -1435,8 +1605,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 291;\n",
-       "                var nbb_unformatted_code = \"from scipy.stats import t as t_dist\\n\\ndef truncated_t_sf(qs, df, mu, sigma):\\n    ps = t_dist.sf(qs, df, mu, sigma)\\n    surv_model = Surv(ps / ps[0], qs)\\n    return surv_model\";\n",
+       "                var nbb_cell_id = 78;\n",
+       "                var nbb_unformatted_code = \"from scipy.stats import t as t_dist\\n\\n\\ndef truncated_t_sf(qs, df, mu, sigma):\\n    ps = t_dist.sf(qs, df, mu, sigma)\\n    surv_model = Surv(ps / ps[0], qs)\\n    return surv_model\";\n",
        "                var nbb_formatted_code = \"from scipy.stats import t as t_dist\\n\\n\\ndef truncated_t_sf(qs, df, mu, sigma):\\n    ps = t_dist.sf(qs, df, mu, sigma)\\n    surv_model = Surv(ps / ps[0], qs)\\n    return surv_model\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -1477,7 +1647,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 292,
+   "execution_count": 79,
    "metadata": {},
    "outputs": [
     {
@@ -1485,9 +1655,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 292;\n",
-       "                var nbb_unformatted_code = \"from scipy.optimize import least_squares\\n\\ndef fit_truncated_t(df, surv):\\n    \\\"\\\"\\\"Given df, find the best values of mu and sigma.\\\"\\\"\\\"\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high, 1000)\\n    ps = np.linspace(0.01, 0.8, 20)\\n    qs = surv.inverse(ps)\\n\\n    def error_func_t(params, df, surv):\\n        # print(params)\\n        mu, sigma = params\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        error = surv(qs) - surv_model(qs)\\n        return error\\n\\n    pmf = surv.make_pmf()\\n    pmf.normalize()\\n    params = pmf.mean(), pmf.std()\\n    res = least_squares(error_func_t, x0=params, args=(df, surv), xtol=1e-3)\\n    assert res.success\\n    return res.x\";\n",
-       "                var nbb_formatted_code = \"from scipy.optimize import least_squares\\n\\n\\ndef fit_truncated_t(df, surv):\\n    \\\"\\\"\\\"Given df, find the best values of mu and sigma.\\\"\\\"\\\"\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high, 1000)\\n    ps = np.linspace(0.01, 0.8, 20)\\n    qs = surv.inverse(ps)\\n\\n    def error_func_t(params, df, surv):\\n        # print(params)\\n        mu, sigma = params\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        error = surv(qs) - surv_model(qs)\\n        return error\\n\\n    pmf = surv.make_pmf()\\n    pmf.normalize()\\n    params = pmf.mean(), pmf.std()\\n    res = least_squares(error_func_t, x0=params, args=(df, surv), xtol=1e-3)\\n    assert res.success\\n    return res.x\";\n",
+       "                var nbb_cell_id = 79;\n",
+       "                var nbb_unformatted_code = \"from scipy.optimize import least_squares\\n\\n\\ndef fit_truncated_t(df, surv):\\n    \\\"\\\"\\\"Given df, find the best values of mu and sigma.\\\"\\\"\\\"\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high, 1000)\\n    ps = np.linspace(0.01, 0.8, 20)\\n    qs = surv.inverse(ps)\\n\\n    def error_func_t(params, df, surv):\\n        mu, sigma = params\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        error = surv(qs) - surv_model(qs)\\n        return error\\n\\n    pmf = surv.make_pmf()\\n    pmf.normalize()\\n    params = pmf.mean(), pmf.std()\\n    res = least_squares(error_func_t, x0=params, args=(df, surv), xtol=1e-3)\\n    assert res.success\\n    return res.x\";\n",
+       "                var nbb_formatted_code = \"from scipy.optimize import least_squares\\n\\n\\ndef fit_truncated_t(df, surv):\\n    \\\"\\\"\\\"Given df, find the best values of mu and sigma.\\\"\\\"\\\"\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high, 1000)\\n    ps = np.linspace(0.01, 0.8, 20)\\n    qs = surv.inverse(ps)\\n\\n    def error_func_t(params, df, surv):\\n        mu, sigma = params\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        error = surv(qs) - surv_model(qs)\\n        return error\\n\\n    pmf = surv.make_pmf()\\n    pmf.normalize()\\n    params = pmf.mean(), pmf.std()\\n    res = least_squares(error_func_t, x0=params, args=(df, surv), xtol=1e-3)\\n    assert res.success\\n    return res.x\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -1543,7 +1713,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 293,
+   "execution_count": 80,
    "metadata": {},
    "outputs": [
     {
@@ -1551,8 +1721,8 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 293;\n",
-       "                var nbb_unformatted_code = \"from scipy.optimize import minimize\\n\\ndef minimize_df(df0, surv, bounds=[(1, 1e3)], ps=None):\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high * 1.2, 2000)\\n\\n    if ps is None:\\n        t = surv.ps[0], surv.ps[-5]\\n        low, high = np.log10(t)\\n        ps = np.logspace(low, high, 30, endpoint=False)\\n\\n    qs = surv.inverse(ps)\\n\\n    def error_func_tail(params):\\n        (df,) = params\\n        print(df)\\n        mu, sigma = fit_truncated_t(df, surv)\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        errors = np.log10(surv(qs)) - np.log10(surv_model(qs))\\n        return np.sum(errors ** 2)\\n\\n    params = (df0,)\\n    res = minimize(error_func_tail, x0=params, bounds=bounds, tol=1e-3, method=\\\"Powell\\\")\\n    assert res.success\\n    return res.x\";\n",
+       "                var nbb_cell_id = 80;\n",
+       "                var nbb_unformatted_code = \"from scipy.optimize import minimize\\n\\n\\ndef minimize_df(df0, surv, bounds=[(1, 1e3)], ps=None):\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high * 1.2, 2000)\\n\\n    if ps is None:\\n        t = surv.ps[0], surv.ps[-5]\\n        low, high = np.log10(t)\\n        ps = np.logspace(low, high, 30, endpoint=False)\\n\\n    qs = surv.inverse(ps)\\n\\n    def error_func_tail(params):\\n        (df,) = params\\n        print(df)\\n        mu, sigma = fit_truncated_t(df, surv)\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        errors = np.log10(surv(qs)) - np.log10(surv_model(qs))\\n        return np.sum(errors**2)\\n\\n    params = (df0,)\\n    res = minimize(error_func_tail, x0=params, bounds=bounds, tol=1e-3, method=\\\"Powell\\\")\\n    assert res.success\\n    return res.x\";\n",
        "                var nbb_formatted_code = \"from scipy.optimize import minimize\\n\\n\\ndef minimize_df(df0, surv, bounds=[(1, 1e3)], ps=None):\\n    low, high = surv.qs.min(), surv.qs.max()\\n    qs_model = np.linspace(low, high * 1.2, 2000)\\n\\n    if ps is None:\\n        t = surv.ps[0], surv.ps[-5]\\n        low, high = np.log10(t)\\n        ps = np.logspace(low, high, 30, endpoint=False)\\n\\n    qs = surv.inverse(ps)\\n\\n    def error_func_tail(params):\\n        (df,) = params\\n        print(df)\\n        mu, sigma = fit_truncated_t(df, surv)\\n        surv_model = truncated_t_sf(qs_model, df, mu, sigma)\\n\\n        errors = np.log10(surv(qs)) - np.log10(surv_model(qs))\\n        return np.sum(errors**2)\\n\\n    params = (df0,)\\n    res = minimize(error_func_tail, x0=params, bounds=bounds, tol=1e-3, method=\\\"Powell\\\")\\n    assert res.success\\n    return res.x\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
@@ -1606,7 +1776,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 307,
+   "execution_count": 81,
    "metadata": {},
    "outputs": [
     {
@@ -1623,43 +1793,41 @@
       "35.407411894884405\n",
       "22.26495001595599\n",
       "14.142461878928419\n",
-      "26.396431469641538\n",
-      "22.378315526830374\n",
-      "23.37711806078531\n",
-      "24.53039316028008\n",
-      "23.209065736046366\n",
-      "23.229227282976307\n",
-      "23.225700629153852\n",
-      "23.225367269503405\n",
-      "23.226033988804296\n",
-      "21.451401258307705\n",
+      "25.283073250551638\n",
+      "19.7236020807297\n",
+      "22.167510053888318\n",
+      "21.970382380734854\n",
+      "21.93000366412791\n",
+      "21.932973281119267\n",
+      "21.93330665994396\n",
+      "21.933640038763702\n",
+      "18.866613319887918\n",
       "382.58404523885497\n",
       "618.4159547611448\n",
-      "236.83190952228992\n",
-      "146.75213571656516\n",
-      "91.07977380572477\n",
+      "236.83190952228986\n",
+      "146.75213571656514\n",
+      "91.07977380572476\n",
       "56.67236191084038\n",
       "35.407411894884405\n",
-      "22.26495001595599\n",
+      "22.264950015955982\n",
       "14.142461878928419\n",
-      "26.396431469641538\n",
-      "22.378315526830374\n",
-      "23.37711806078531\n",
-      "24.53039316028008\n",
-      "23.209065736046366\n",
-      "23.229227282976307\n",
-      "23.225700629153852\n",
-      "23.22536729582052\n",
-      "23.22503396248224\n"
+      "25.283073250516892\n",
+      "19.723601830671786\n",
+      "22.167510080319087\n",
+      "21.97038323398375\n",
+      "21.93000166466634\n",
+      "21.932975865105618\n",
+      "21.933309198443858\n",
+      "21.932642531767378\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "array([23.2253673])"
+       "array([21.93297587])"
       ]
      },
-     "execution_count": 307,
+     "execution_count": 81,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -1668,7 +1836,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 307;\n",
+       "                var nbb_cell_id = 81;\n",
        "                var nbb_unformatted_code = \"df = minimize_df(25, surv)\\ndf\";\n",
        "                var nbb_formatted_code = \"df = minimize_df(25, surv)\\ndf\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1698,16 +1866,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 308,
+   "execution_count": 82,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(array([23.2253673]), 6.431987258334933, 0.4916380552135185)"
+       "(array([21.93297587]), 6.430927981834091, 0.48910465307252876)"
       ]
      },
-     "execution_count": 308,
+     "execution_count": 82,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -1716,7 +1884,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 308;\n",
+       "                var nbb_cell_id = 82;\n",
        "                var nbb_unformatted_code = \"mu, sigma = fit_truncated_t(df, surv)\\ndf, mu, sigma\";\n",
        "                var nbb_formatted_code = \"mu, sigma = fit_truncated_t(df, surv)\\ndf, mu, sigma\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1753,7 +1921,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 389,
+   "execution_count": 83,
    "metadata": {},
    "outputs": [
     {
@@ -1761,9 +1929,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 389;\n",
-       "                var nbb_unformatted_code = \"low, high = surv.qs.min(), surv.qs.max()\\nqs = np.linspace(low, 1.1 * high, 2000)\\nsurv_model = truncated_t_sf(qs, df, mu, sigma)\";\n",
-       "                var nbb_formatted_code = \"low, high = surv.qs.min(), surv.qs.max()\\nqs = np.linspace(low, 1.1 * high, 2000)\\nsurv_model = truncated_t_sf(qs, df, mu, sigma)\";\n",
+       "                var nbb_cell_id = 83;\n",
+       "                var nbb_unformatted_code = \"low, high = surv.qs.min(), surv.qs.max()\\nqs = np.linspace(low, 11, 2000)\\nsurv_model = truncated_t_sf(qs, df, mu, sigma)\";\n",
+       "                var nbb_formatted_code = \"low, high = surv.qs.min(), surv.qs.max()\\nqs = np.linspace(low, 11, 2000)\\nsurv_model = truncated_t_sf(qs, df, mu, sigma)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -1786,18 +1954,18 @@
    ],
    "source": [
     "low, high = surv.qs.min(), surv.qs.max()\n",
-    "qs = np.linspace(low, 1.1 * high, 2000)\n",
+    "qs = np.linspace(low, 11, 2000)\n",
     "surv_model = truncated_t_sf(qs, df, mu, sigma)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 390,
+   "execution_count": 84,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -1810,7 +1978,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 390;\n",
+       "                var nbb_cell_id = 84;\n",
        "                var nbb_unformatted_code = \"surv_model.plot(color=\\\"gray\\\", alpha=0.4, label=\\\"model\\\")\\nsurv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (log10 words per appearance)\\\", ylabel=\\\"Tail probability\\\")\";\n",
        "                var nbb_formatted_code = \"surv_model.plot(color=\\\"gray\\\", alpha=0.4, label=\\\"model\\\")\\nsurv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(xlabel=\\\"Inverse rate (log10 words per appearance)\\\", ylabel=\\\"Tail probability\\\")\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1850,12 +2018,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 391,
+   "execution_count": 85,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -1868,7 +2036,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 391;\n",
+       "                var nbb_cell_id = 85;\n",
        "                var nbb_unformatted_code = \"surv_model.plot(color=\\\"gray\\\", alpha=0.4, label=\\\"model\\\")\\nsurv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Tail probability\\\",\\n    yscale=\\\"log\\\",\\n)\";\n",
        "                var nbb_formatted_code = \"surv_model.plot(color=\\\"gray\\\", alpha=0.4, label=\\\"model\\\")\\nsurv.plot(marker=\\\".\\\", ms=1, lw=0.2, label=\\\"data\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Tail probability\\\",\\n    yscale=\\\"log\\\",\\n)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -1905,27 +2073,29 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Make a Prior"
+    "The model fits the data well in the extreme tail, which is exactly where we need it.\n",
+    "And we can use the model to extrapolate a little beyond the data, to make sure we cover the range that will turn out to be likely in the scenario where we hear a word for this first time after 50 years."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## The Update\n",
+    "\n",
+    "The model we've developed is the distribution of inverse rates for the words that appear in the corpus and, by extrapolation, for additional rare words that didn't appear in the corpus.\n",
+    "This distribution will be the prior for the Bayesian update.\n",
+    "We just have to convert it from a survival function to a PMF (remembering that these are equivalent representations of the same distribution)."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 394,
+   "execution_count": 86,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "text/plain": [
-       "<Axes: >"
-      ]
-     },
-     "execution_count": 394,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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zMVrjem8hxsttuOh0uiFHKk1NTWi12jG30Wq1Q5aZTCbi4+MBuH79Ops3b+aHP/whTzzxhKtNVFQUwcGD0y3T09PRarXU1tYOqy03N5eamhrXIyIiYkw7LYSvqW+/xuKouQT6T98ET+fkAQkXMRFuf1JTU1MxmUzU1NQAUFhYSGZm5pA2GzdupLS0lLa2NqxWK4cOHXK1yczMpKCgAICSkhL0ej1RUVEMDAyQmZnJI488wrPPPjtke62tra5/V1dX09jYyJIlSya3p0L4sIb2qbv75EiiNIGEBwdwoUO6xcT4+btroFarKSgoICsrC4vFQnp6Otu3b6e4uJji4mIKCgoIDw/nwIEDpKWlYbfb2bp1Kxs2bABg7969bNu2jaSkJEJDQzl8+DAwOHX55MmTXLp0iTfffBOAF154gaysLF599VXeeustAgICCAgI4ODBg3JUImatq303udJ7c9qmITupVCqZMSYmTOWYzICJlzEYDK4jLCFmik8vXmXrbz7m5SdT+HZK/LS+909/X8WblS3U7NuIegov8y9802jfuXKGvhBebjpubTwSfYwGi9VOS9eNaX9v4dskXITwcvWXe/FTwZLo6Zsp5pQYM/ieDR1yjTExPhIuQni5hvZeEuaHMCdAPe3vrY+WqyOLiZFwEcLLNbT3olegSwwgPiKYIH8/CRcxbhIuQngxc/8Al8z903rZl9up/VQsiZYZY2L8JFyE8GLTeffJkehjNFzo6JvUlTjE7CPhIoQXc16wcrrPcbmdPlpDz40BrvTeVKwG4XskXITwYs5pyM7rfCnBNWNMusbEOEi4COHF6tt7iZ8XzNwgtxfTmDKua4zJXSnFOEi4COHF6i/3KjaY73RP1Fz8VMhdKcW4SLgI4aX6LFZaum8oOpgPEOSvJmF+iHSLiXGRcBHCS31162rESlz25U5yAUsxXhIuQngp52C+XuFuMYDEGA2XzP30WqxKlyJ8hISLEF7KeWtjJachOzlnq8m4ixgrCRchvFT95V4WhAURNidA6VLkrpRi3CRchPBSDe3XvGK8BWQ6shg/CRchvFD/gI2mq9e9oksMIGxOADGhQXLkIsZsTOFSVlaG0WhEr9eTk5ODzWYb1ubo0aMkJyeTmJhIXl6e63Wz2UxGRgZJSUmkpqZy/vx5ACorK1m3bh1Go5EVK1bwyiuvuNaxWq3s2rULvV6P0Wjk1KlTk91PIXzKVx192B0ofo7L7fQxGhlzEWPmNlzsdjs5OTkcO3aMhoYGzGYzR44cGdKmp6eHPXv2UF5eTm1tLaWlpZSXlwOwf/9+Vq5cSX19Pfv27WP37t0AhISE8Prrr1NdXc1HH33Er371KyorKwE4ePAgFouFhoYG3njjDbKzs+WieWJWUfLukyPRx2j4+up1blrtSpcifIDbcKmoqCAuLg6DwQBAdnY2RUVFQ9qcOHGC9evXExsbi7+/Pzt27HC1KSoqIicnB4BNmzZRV1dHZ2cnycnJLF26FICwsDCWL19Oc3PzsHVWrVpFZGQkZ8+e9dAuC+H9vOFqyHfSx2iw2R00dvYpXYrwAW7DxWQyodPpXM8TEhJcITCWNncu02q1mEymIetfuHCBP/7xj6xbt27M7wmQn5+PwWBwPbq6utztjhA+oaG9lyhNIBFzA5UuxcU5/lN/WbrGhHtuw2Us3VGT6bLq7u7m8ccf5+WXX2b+/Pnj2l5ubi41NTWuR0RExITrEMKb1Lf3es1gvpOzi87ZZSfEaNyGi06nG3LU0NTUhFarHXMbrVY7ZJnJZCI+Ph6A69evs3nzZn74wx/yxBNPjOs9hZipblrtNF7p87pwidIEMi8kwHVypxCjcRsuqampmEwmampqACgsLCQzM3NIm40bN1JaWkpbWxtWq5VDhw652mRmZlJQUABASUkJer2eqKgoBgYGyMzM5JFHHuHZZ58dsr3b16mqqqKjo4O1a9dOfm+F8AFfd/ZhtTu8ajAfQKVSkRwT6rqBmRCjcRsuarWagoICsrKySExMRKPRsH37doqLi12D7uHh4Rw4cIC0tDSWLl1Keno6GzZsAGDv3r1UVVWRlJTECy+8wGuvvQYMTl0+efIkb775JikpKaSkpPD73/8egJ07dxIQEIBer+fJJ5+ksLAQlUo1VZ+BEF7Fmy77cif9Ag1fXenFapMZY2J0KscMmuNrMBhcR1hC+KqX3q3jpXfr+TTvG8SEzlG6nCH+14cX+bvjNbz7XLpXhp+YXqN958oZ+kJ4mfrLvcwLCSBaE6R0KcM4u+oaZFBfuCHhIoSXqW+/RnJMqFd2BTuvGCDTkYU7Ei5CeJEBm52LV/q86rIvt4sJDSJsjr/MGBNuSbgI4UUar/QxYHN41Zn5t1OpVCQtCJVwEW5JuAjhRepudTclL/Cuaci3S4rRcKGjF5t9xswFElNAwkUIL+K6YKUXh4s+RsNNq52mq9eVLkV4MQkXIbxI/eVeIkICiNJ4zzXF7uQMvvrLMmNMjEzCRQgvUnd58O6T3jhTzCnZOWNMxl3EKCRchPASN63ePVPMaWHYHDRB/nJXSjEqCRchvITzmmLePJgPgzPG9DEauTqyGJWEixBewjlTzNuPXGBwxlhDey92mTEmRiDhIoSXqLvsfbc2HknSAg39A3ZMXTeULkV4KQkXIbxEQ7v3zxRzcs0Yk64xMQIJFyG8RN3layQt8O6ZYk7OKwjIjDExEgkXIbyAc6ZYsg+MtwDEhQcTEqim7pIcuYi7k3ARwgs0eundJ0fi56di6cJQvpRwESMYU7iUlZVhNBrR6/Xk5ORgs9mGtTl69CjJyckkJiaSl5fnet1sNpORkUFSUhKpqamcP3/etWzr1q1ER0ej1+uHbOvgwYNERka67lCZm5s70f0Twic4v6SXLfSNcAFYtjCMhvZeBuSulOIu3IaL3W4nJyeHY8eO0dDQgNls5siRI0Pa9PT0sGfPHsrLy6mtraW0tJTy8nIA9u/fz8qVK6mvr2ffvn3s3r3btd4zzzzDO++8c9f33bJlC5WVlVRWVpKfnz+ZfRTC651vMwODX9i+YnlsKDdv3SJAiDu5DZeKigri4uIwGAwAZGdnU1RUNKTNiRMnWL9+PbGxsfj7+7Njxw5Xm6KiInJycgDYtGkTdXV1dHZ2AvDwww8zf/58j+6QEL7oyzYzceFzCA8JULqUMXMGoTMYhbid23AxmUzodDrX84SEBJqbm8fc5s5lWq0Wk8nktrDjx4+zevVqHn30USoqKtzviRA+7MtL11gW6ztHLQBLb3XhybiLuBu34eJwuD8DdyxtxuOxxx6jsbGRzz//nLy8PLZs2UJv7/Apj/n5+RgMBtejq6vLo3UIMR26r9+kraef5bG+M94CEB4cQPy8YDlyEXflNlx0Ot2QI5Wmpia0Wu2Y22i12iHLTCYT8fHxo75nVFQUwcHBAKSnp6PVaqmtrR3WLjc3l5qaGtcjIiLC3e4I4XXOtzkH833ryAUGJyB82SZHLmI4t+GSmpqKyWSipqYGgMLCQjIzM4e02bhxI6WlpbS1tWG1Wjl06JCrTWZmJgUFBQCUlJSg1+uJiooa9T1bW1td/66urqaxsZElS5aMb8+E8BFfXhr8y9/XjlwAlsWGcsncT1ffTaVLEV7Gbbio1WoKCgrIysoiMTERjUbD9u3bKS4udg3Uh4eHc+DAAdLS0li6dCnp6els2LABgL1791JVVUVSUhIvvPACr732mmvbmzdv5oEHHqCxsRGtVsuLL74IwKuvvorRaCQlJYWdO3dy8OBBOSoRM9aXbdcI9PdjceRcpUsZt+W3xolk3EXcSeXw9ICJggwGg+sISwhf8e1XP8DugON/8aDSpYxbQ3sv3/xlOf8jw8CudfcoXY6YZqN958oZ+kIoyGZ3UHv5mk+dPHm7xZEhBPn7ybiLGEbCRQgFNXb20T9g97lpyE7+aj+SF4S6xo2EcJJwEUJBzr/4l/vokQsMzhirvXwNm9w4TNxGwkUIBbku++KjRy4wWHv/gFwGRgwl4SKEgqpbe4gNn8P8ud5/g7CRGOMGg7G6tUfhSoQ3kXARQiEOh4NzLWZWxIcrXcqkOMPlnEnCRfyJhIsQCrlstnCl18JKHw+X0DkBLImay7kWCRfxJxIuQijE+WXs6+ECsCI+nOpWM3YZ1Be3SLgIoRBnuBjjfXcw32llfDi9FiuNnTKoLwZJuAihkC9aelgQFkRM6BylS5k057iRdI0JJwkXIRRyrqVnRnSJwZ+Ovqpb5WRKMUjCRQgFXDb303HN4vMzxZzC5gRwT9RcmTEmXCRchFDAFzNoMN9pRXw4X7T2ePzmgcI3SbgIoYCZNFPMaWV8GNf6rXzdeV3pUoQXkHARQgFVpluD+WG+P5jv5Oziq5JBfYGEixDTzuFwcLapizW6mXUDvJXx4ahUUNnUrXQpwgtIuAgxzRo7r9N1fYA1CfOULsWjQucEsHRBKGeaupQuRXiBMYVLWVkZRqMRvV5PTk4ONpttWJujR4+SnJxMYmIieXl5rtfNZjMZGRkkJSWRmprK+fPnXcu2bt1KdHQ0er1+yLasViu7du1Cr9djNBo5derURPdPCK9z9taX79pFM+vIBWBNQgTVrT30Dwz/jhCzi9twsdvt5OTkcOzYMRoaGjCbzRw5cmRIm56eHvbs2UN5eTm1tbWUlpZSXl4OwP79+1m5ciX19fXs27eP3bt3u9Z75plneOedd4a958GDB7FYLDQ0NPDGG2+QnZ0tM1DEjHGmqQt/PxUr4mbOYL7T2oR5DNgccoVk4T5cKioqiIuLw2AwAJCdnU1RUdGQNidOnGD9+vXExsbi7+/Pjh07XG2KiorIyckBYNOmTdTV1dHZ2QnAww8/zPz584e95+3rrFq1isjISM6ePTuJ3RTCe5xt6mZ5bBjBgWqlS/E459HYma+7lS1EKM5tuJhMJnQ6net5QkICzc3NY25z5zKtVovJZJr0ewrhi67ftPLlpWusnWHjLU5LouYyLyRAxl0E/u4ajKU7ytNdVmPdXn5+Pvn5+a7nXV3yAy28W5WpB5vdwZqEmTfeAqBSqVijm8eZpi4cDgcqlUrpkoRC3B656HS6IUcNTU1NaLXaMbfRarVDlplMJuLj4yf9ngC5ubnU1NS4HhERM/MXVswcZ29N0107Q8MFBvftstlCa0+/0qUIBbkNl9TUVEwmEzU1NQAUFhaSmZk5pM3GjRspLS2lra0Nq9XKoUOHXG0yMzMpKCgAoKSkBL1eT1RU1Kjvefs6VVVVdHR0sHbt2vHvnRBe5tOLnURpgtDND1a6lCnjHHf57GvpSZjN3IaLWq2moKCArKwsEhMT0Wg0bN++neLiYtege3h4OAcOHCAtLY2lS5eSnp7Ohg0bANi7dy9VVVUkJSXxwgsv8Nprr7m2vXnzZh544AEaGxvRarW8+OKLAOzcuZOAgAD0ej1PPvkkhYWFcngtfJ7N7uCPjV3cv2T+jP55TtHNQ+2nouLiVaVLEQpSOWbQHF+DweA6whLC25wz9ZDx6gf8z8dXsP3+RUqXM6W2vPYhvf1WTj6XrnQpYgqN9p0rZ+gLMU1OXxycgn//PcOn38809y+JpL69lyu9FqVLEQqRcBFimnzy1VUi5waij9EoXcqUu39JJACffNWpcCVCKRIuQkwDm93Bpxc7ufeemT3e4pS6KAK1n0rCZRaTcBFiGnx5yYy538p9s6BLDGBukD+rtOF88pUM6s9WEi5CTAPnl+x9t7qLZoP7l0TS0N5LxzUZd5mNJFyEmAbv13UQpQli6YJQpUuZNs5xl48uXFG4EqEECRchplj/gI3TFztJS4rCz2/mj7c43bt4PoH+fpTXdShdilCAhIsQU6yi8Sr9A3bSl0YrXcq0Cg5Uc/+SSN6v68BunzGn04kxknARYoqV13agUsGD+tEvezQTrU+O5krvTapbzUqXIqaZhIsQU+z9+g5WxocTqQlSupRpt/7W0VpZbbvClYjpJuEixBRq67lB3eVe0pJmV5eY0z1Rc0mYH0KZjLvMOhIuQkyhkzWXAdiwLEbhSpShUqnYsDSas01ddF+/qXQ5YhpJuAgxhd6pvkRMaBBrdPOULkUx65fFYHdAqXSNzSoSLkJMke7rN/nkq6s8Ylgwq6Yg3+nPEyMJnePPf5y7pHQpYhpJuAgxRf7zfDs2u4P/alyodCmKCvJX883lCyiv66DPYlW6HDFNJFyEmCLvVF8idI6/60z12ey/rViIxWqXrrFZRMJFiClwrX+A8roOvrEshkB/+TVLS45mbqBausZmkTH91JeVlWE0GtHr9eTk5GCz2Ya1OXr0KMnJySQmJpKXl+d63Ww2k5GRQVJSEqmpqZw/f97tOj/72c+IjY0lJSWFlJQU/v7v/34y+yjEtPuPLy5hsdr59pp4pUvxCnMC1Dy8fAHvfdkuXWOzhNtwsdvt5OTkcOzYMRoaGjCbzRw5cmRIm56eHvbs2UN5eTm1tbWUlpZSXl4OwP79+1m5ciX19fXs27eP3bt3u10HIDc3l8rKSiorK4cEjxC+4N/PtBClCeShWXhW/kgeT4njxoCN//hCjl5mA7fhUlFRQVxcHAaDAYDs7GyKioqGtDlx4gTr168nNjYWf39/duzY4WpTVFRETk4OAJs2baKuro7Ozs5R1xHCl7V23+CTi51krI7DXy1dYk5pydFEaYL4/WfNSpcipoHbn3yTyYROp3M9T0hIoLm5ecxt7lym1WoxmUxut/sv//IvrFq1ii1btlBfX3/X2vLz8zEYDK5HV1eXu90RYsq9VdmKwwGZa7RKl+JVAtR+bFkTxydfXaX56nWlyxFTzG24OBzur2Y6ljbjWeeZZ57hwoULVFVV8eSTT5KRkXHXdrm5udTU1LgeERER465DCE+y2x38rqKJpBgNK+LDlC7H63znzwYD9/efmRSuREw1t+Gi0+mGHFE0NTWh1WrH3Ear1Q5ZZjKZiI+PH3WdhQsXEhAQAMB3v/tduru76eyUe3EL73eq4QqNndfZ/sAiVKrZe+LkSJYtDGOVNpyjf2xmwGZXuhwxhdyGS2pqKiaTiZqaGgAKCwvJzMwc0mbjxo2UlpbS1taG1Wrl0KFDrjaZmZkUFBQAUFJSgl6vJyoqatR1WltbXdsuLS0lICCA+fNnx73HhW87/HEjcwPVbJFZYiPa+eeLaevp54QM7M9o/u4aqNVqCgoKyMrKwmKxkJ6ezvbt2ykuLqa4uJiCggLCw8M5cOAAaWlp2O12tm7dyoYNGwDYu3cv27ZtIykpidDQUA4fPgww6jrPP/88Z8+eRa1WExoayr/927/JX4HC6zVfvc5/ftnOtvsSCJ0ToHQ5Xmvzqlh+XvIlr394kYzVcUqXI6aIyjGRARMvZTAYXEdYQky3v33rC3778de8+1wa+phQpcvxai+/W88/v1vHv+/+c9YkyFiprxrtO1fmSQrhAe3X+vnfFc1sNC6UYBmDbfcnEOTvx2tlF5QuRUwRCRchPKDw1EVuWu3kbtArXYpPiNIEse2+RZysuUyVqVvpcsQUkHARYpIu9fRz6ONG0pOjWakNV7ocn/Gj9YnMCfDjn0/WKV2KmAISLkJM0i9P1mKx2tm7canSpfiU6NAgdjywmNLaDj69eFXpcoSHSbgIMQk1rWaOfWbiO2u1GOPkqGW8frQ+kYiQAP72rS+wynkvM4qEixATZLM7+Jt/P0dwgJo9j8pRy0TMCwnkpxuX8eWla/z246+VLkd4kISLEBP0vz68yOfN3fx04zIWhs9RuhyftTVVx2rdPH55sk6uOTaDSLgIMQF1l6/xiz/Ukroogu33L1K6HJ/m56fiQNYqBmx2fvK/z0r32Awh4SLEOPVZrPzoyGcE+PnxiydW4+cnV4+YrOQFofx/m5Zzpqmbl969+1XQhW+RcBFiHGx2B88dreRCRx8HnljF4qi5Spc0Y3z/gUU8YljAq6UNvFXZonQ5YpIkXIQYI4fDwc+Kq3mn+jI/3qBn44pYpUuaUVQqFf/83RSWx4bx18eq+PiCXAndl0m4CDEGdvtgsBz+5Guy/kzLXz2arHRJM5ImyJ/Xd6YSpQlk18FP+aD+itIliQmScBHCjf4BG//v0UoOffw1mWvj+YfMlXKV7ikUGx7M755+gChNED84VMGbZ6WLzBdJuAgxiotX+tjy2ke8VdnKD9bdwy+yVuOvll+bqaabH8LRpx8gMVrDX/6ukp8VV9M/YFO6LDEO8lsixF3ctNrJL21g40vvc/FKL//83dX8bYZBZoZNo7h5wfzbj/6cb6fEcfCjRv7by6f46IJ0k/kKtzcLE2I2sVht/P4zE6+VXqCl+wYPLInk77esYEm0RunSZqXgQDUvfTeFRw0L+R/FX/C9//80acnR/OQbSaxNmCfdk15sTEcuZWVlGI1G9Ho9OTk52GzDD0+PHj1KcnIyiYmJ5OXluV43m81kZGSQlJREamoq58+fn9Q6Qnia3e6gytTN3x2v5v6f/yd5//4FcwL8ePnJFP71h/dJsChMpVKxeVUs//ncenavT6Ti4lW+8+uP2PzKB/z240Yu9fQrXaK4C7d3orTb7SQnJ1NcXIzBYGDr1q1s3ryZHTt2uNr09PSwcuVKTp8+TXR0NGlpabz44oukp6fzwgsvYLfb+fnPf05JSQkHDhygtLR0Quu4I3eiFGNhsdqovXSNcy09fPZ1F+/XXeFKrwWVCtYlRvH/3JvAxhULUUsXmFe60mvhdxXNvPFpE6auGwAY48JYp49itXYeKQnziAufI0c102C071y34XL69Gn++q//mvfffx+Ad955h/z8fIqLi11tfve73/H222/z29/+FoDf/OY3VFdX88orr7B8+XLefvttlixZAkB8fDxVVVW8++67414nMjJywjsqZiaHw8GAzYHFasNitdM/YKPnxgA91wfovjFA1/WbdPXdpKX7Bs1Xb9DcdZ2WrhtY7YM/9kH+fty/JJL1S6N5xLAAbUSIwnskxspud/BZUxfvfdnOe+fbqb18zbVsbqCaRZFzWRwVQvy8YKI0QURqgojUBBIREsjcQDXBgWpCAv0JCVQT5O8nYTQBo33nuh1zMZlM6HQ61/OEhASam5vdtjlx4sRdl2m1Wkwm04TWcRcuE2WzO3jyXz52Pb8zbm9/emcW35nMo61758LR1nXcsXTYdoe0vXPZyH8vDK9v5Pdxt13HiE9GX9f9Z+YYeZkDLFY7FquNm1Y7FuvYrkMVqPYjPiKYhPkhPJQUhTEunJXx4SQvCCXQX+a1+CI/PxX/ZfF8/svi+fx04zJ6bgxwztTD56ZuLnT08nXndU5/dZXOvpvut6WCIH81/n4q1GoV/n4q/P38UPup8FerBv/rp8LvVgA5g0gFODNJpQIVqtv+/aeFQ9qNsL4Svrl8AU+nJ07Jtt2Gi5sDmzG38cQ6d8rPzyc/P9/1vKura8LbunHHNEfnD4nruer2ZXe446dDdce/XYtVd26VYX8tDVn3jsbD1h6lptHWHbZsHG3vdHv97mu4+3ru1x1aT6C/H0Gux+BfnYG3PQ8PDiA8JIB5wQFEzA1kXnAAUZogmek1w4UHB/BgUhQPJkUNed1itXG17yadvTe50muh6/pNrt+0ceOmjT6LjesDVm7ctGEZsGNzOLDa7FjtDmx2xx3/tWOzO1x/8Dhc/zP4B9Htrzscf/oTyeFwvjb4Pw7nGo7hf9xNN+cR/FRwGy46nW7IkUpTUxNarXZYm6qqqru20Wq1NDc3u7q4TCYT8fHxE1rnTrm5ueTm5rqeGwwG93t8F2o/Ff/nLx6a0LpCCO8W5K8mNjyY2PBgpUuZVdz2B6SmpmIymVz9aoWFhWRmZg5ps3HjRkpLS2lra8NqtXLo0CFXm8zMTAoKCgAoKSlBr9cTFRU1oXWEEEL4BrdHLmq1moKCArKysrBYLKSnp7N9+3aKi4spLi6moKCA8PBwDhw4QFpaGna7na1bt7JhwwYA9u7dy7Zt20hKSiI0NJTDhw8DTGgdIYQQvsHtbDFfIrPFhBBi+oz2nSvTZIQQQnichIsQQgiPk3ARQgjhcRIuQgghPG5GDeiHhYUNOwfH23R1dREREaF0GV5JPpuRyWczMvlsRjeVn4/JZMJsNt912YwKF18gM9pGJp/NyOSzGZl8NqNT6vORbjEhhBAeJ+EihBDC4yRcptnt10ITQ8lnMzL5bEYmn83olPp8ZMxFCCGEx8mRixBCCI+TcBFCCOFxEi7TpLm5mW984xssX74co9HI3/zN3yhdklfKzc3F39/txbpnlb6+Pnbs2MHSpUtZtmwZv/nNb5QuyWscOXKEVatWkZKSwkMPPURtba3SJSnmJz/5CVqtdtjvz/PPP49eryc5OZmioqLpK8ghpkVra6ujoqLC4XA4HBaLxfHggw863nzzTYWr8i7vv/++4/vf/75DrVYrXYpXefrppx3/+I//6HA4HA673e64fPmywhV5h76+Psf8+fMdHR0dDofD4fj1r3/tyMrKUrgq5Zw6dcrR1tY25Pfn5MmTjoceeshhtVodJpPJodPpHNeuXZuWeuTIZZrExsaSmpoKQGBgIGvWrKGpqUnhqryHxWLh+eef5xe/+IXSpXiVa9euUVxczHPPPQcM3h46JiZG4aq8g91ux+Fw0NvbC0BPTw+xsbEKV6WcBx98kIULFw55raioiJ07d6JWq4mPj2fdunX84Q9/mJZ6pP9BAVevXuXNN9+ctv+TfcG+ffvIzs4mOjpa6VK8yldffcWCBQv48Y9/zKeffsqiRYt46aWXWLRokdKlKU6j0fDqq6+yYsUKwsPDCQ8P5+OPP1a6LK9iMpmG3Dk4ISFhyG3rp5IcuUyzmzdvkpWVxU9+8hOWLVumdDleoaqqitOnT7Nr1y6lS/E6VquVyspKsrKyOHPmDBkZGfzgBz9QuiyvMDAwwGuvvUZFRQUtLS1kZWXx05/+VOmyvIpDwTNNJFymkc1m43vf+x4pKSn81V/9ldLleI0PP/yQmpoa7rnnHhYvXozNZmPx4sUjXhBvNtFqtURGRvLNb34TgCeffJLPPvtM4aq8Q2VlJQ6Hg+XLlwODn81HH32kcFXeRafTDTlSaWpqmraL+0q4TKOnnnqK0NBQ/umf/knpUrzKj370I1pbW2lsbKSxsRG1Wk1jYyNhYWFKl6a4BQsWYDQaOXPmDAAnT57EaDQqXJV30Gq11NbW0tLSAgx+NgaDQeGqvEtmZiYHDx7EZrPR0tLCBx98wKOPPjot7y1jLtPkww8/5PXXX2fFihWsWbMGgB/84Ac8++yzClcmvN2vf/1rsrOz6evrY968eRQUFChdkleIjY3lH/7hH3jkkUcICAggOjqa119/XemyFPP000/z9ttvY7PZ0Gq1fPvb3yY/P5+TJ0+SnJyMn58fv/zlLwkNDZ2WeuTyL0IIITxOusWEEEJ4nISLEEIIj5NwEUII4XESLkIIITxOwkUIIYTHSbgIIYTwOAkXIYQQHifhIoQQwuP+L/4kAKwhJqNDAAAAAElFTkSuQmCC",
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",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -1938,9 +2108,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 394;\n",
-       "                var nbb_unformatted_code = \"prior = surv_model.make_pmf()\\nprior.plot()\";\n",
-       "                var nbb_formatted_code = \"prior = surv_model.make_pmf()\\nprior.plot()\";\n",
+       "                var nbb_cell_id = 86;\n",
+       "                var nbb_unformatted_code = \"prior = surv_model.make_pmf()\\nprior.plot(label=\\\"prior\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Density\\\",\\n)\";\n",
+       "                var nbb_formatted_code = \"prior = surv_model.make_pmf()\\nprior.plot(label=\\\"prior\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Density\\\",\\n)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -1963,47 +2133,33 @@
    ],
    "source": [
     "prior = surv_model.make_pmf()\n",
-    "prior.plot()"
+    "prior.plot(label=\"prior\")\n",
+    "decorate(\n",
+    "    xlabel=\"Inverse rate (log10 words per appearance)\",\n",
+    "    ylabel=\"Density\",\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Update It"
+    "To compute the likelihood of the observation, we have to transform the inverse rates to probabilities."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 384,
+   "execution_count": 87,
    "metadata": {},
    "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "count    2.000000e+03\n",
-       "mean     2.753817e-03\n",
-       "std      8.012930e-03\n",
-       "min      3.162278e-10\n",
-       "25%      3.578765e-08\n",
-       "50%      4.050083e-06\n",
-       "75%      4.583447e-04\n",
-       "max      5.187022e-02\n",
-       "dtype: float64"
-      ]
-     },
-     "execution_count": 384,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
     {
      "data": {
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 384;\n",
-       "                var nbb_unformatted_code = \"ps = 1 / np.power(10, prior.qs)\\ndescribe(ps)\";\n",
-       "                var nbb_formatted_code = \"ps = 1 / np.power(10, prior.qs)\\ndescribe(ps)\";\n",
+       "                var nbb_cell_id = 87;\n",
+       "                var nbb_unformatted_code = \"ps = 1 / np.power(10, prior.qs)\";\n",
+       "                var nbb_formatted_code = \"ps = 1 / np.power(10, prior.qs)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -2025,13 +2181,20 @@
     }
    ],
    "source": [
-    "ps = 1 / np.power(10, prior.qs)\n",
-    "describe(ps)"
+    "ps = 1 / np.power(10, prior.qs)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now suppose that in a given day, you read or hear 10,000 words in a context where you would notice if you heard a new word for the first time.\n",
+    "Here's the number of words you would hear in 50 years."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 385,
+   "execution_count": 88,
    "metadata": {},
    "outputs": [
     {
@@ -2040,7 +2203,7 @@
        "182500000"
       ]
      },
-     "execution_count": 385,
+     "execution_count": 88,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -2049,9 +2212,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 385;\n",
-       "                var nbb_unformatted_code = \"words_per_day = 10_000\\ndays = 50 * 365\\ndays * words_per_day\";\n",
-       "                var nbb_formatted_code = \"words_per_day = 10_000\\ndays = 50 * 365\\ndays * words_per_day\";\n",
+       "                var nbb_cell_id = 88;\n",
+       "                var nbb_unformatted_code = \"words_per_day = 10_000\\ndays = 50 * 365\\nk = days * words_per_day\\nk\";\n",
+       "                var nbb_formatted_code = \"words_per_day = 10_000\\ndays = 50 * 365\\nk = days * words_per_day\\nk\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -2075,40 +2238,31 @@
    "source": [
     "words_per_day = 10_000\n",
     "days = 50 * 365\n",
-    "days * words_per_day"
+    "k = days * words_per_day\n",
+    "k"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now, what's the probability that you fail to hear a word in `k` attempts and then hear it on the next attempt?\n",
+    "We can answer that with the negative binomial distribution, which computes the probability of getting the `n`th success after `k` failures."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 386,
+   "execution_count": 89,
    "metadata": {},
    "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "count    2.000000e+03\n",
-       "mean     2.733730e-10\n",
-       "std      5.653541e-10\n",
-       "min      0.000000e+00\n",
-       "25%      0.000000e+00\n",
-       "50%      0.000000e+00\n",
-       "75%      5.216238e-11\n",
-       "max      2.015761e-09\n",
-       "dtype: float64"
-      ]
-     },
-     "execution_count": 386,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
     {
      "data": {
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 386;\n",
-       "                var nbb_unformatted_code = \"from scipy.stats import nbinom\\n\\nk = days * words_per_day\\nn = 1\\n\\nlikelihood = nbinom.pmf(k, n, ps)\\ndescribe(likelihood)\";\n",
-       "                var nbb_formatted_code = \"from scipy.stats import nbinom\\n\\nk = days * words_per_day\\nn = 1\\n\\nlikelihood = nbinom.pmf(k, n, ps)\\ndescribe(likelihood)\";\n",
+       "                var nbb_cell_id = 89;\n",
+       "                var nbb_unformatted_code = \"from scipy.stats import nbinom\\n\\nn = 1\\n\\nlikelihood = nbinom.pmf(k, n, ps)\";\n",
+       "                var nbb_formatted_code = \"from scipy.stats import nbinom\\n\\nn = 1\\n\\nlikelihood = nbinom.pmf(k, n, ps)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -2132,25 +2286,30 @@
    "source": [
     "from scipy.stats import nbinom\n",
     "\n",
-    "k = days * words_per_day\n",
     "n = 1\n",
     "\n",
-    "likelihood = nbinom.pmf(k, n, ps)\n",
-    "describe(likelihood)"
+    "likelihood = nbinom.pmf(k, n, ps)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With this likelihood and the prior, we can compute the posterior distribution in the usual way."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 387,
+   "execution_count": 90,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "1.3558684208624722e-11"
+       "1.3468326547799861e-11"
       ]
      },
-     "execution_count": 387,
+     "execution_count": 90,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -2159,7 +2318,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 387;\n",
+       "                var nbb_cell_id = 90;\n",
        "                var nbb_unformatted_code = \"posterior = prior * likelihood\\nposterior.normalize()\";\n",
        "                var nbb_formatted_code = \"posterior = prior * likelihood\\nposterior.normalize()\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -2187,24 +2346,21 @@
     "posterior.normalize()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And here's what it looks like."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 388,
+   "execution_count": 91,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "text/plain": [
-       "<Axes: >"
-      ]
-     },
-     "execution_count": 388,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 450x262.5 with 1 Axes>"
       ]
@@ -2217,9 +2373,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 388;\n",
-       "                var nbb_unformatted_code = \"posterior.plot()\";\n",
-       "                var nbb_formatted_code = \"posterior.plot()\";\n",
+       "                var nbb_cell_id = 91;\n",
+       "                var nbb_unformatted_code = \"prior.plot(alpha=0.5, label=\\\"prior\\\")\\nposterior.plot(label=\\\"posterior\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Density\\\",\\n)\";\n",
+       "                var nbb_formatted_code = \"prior.plot(alpha=0.5, label=\\\"prior\\\")\\nposterior.plot(label=\\\"posterior\\\")\\ndecorate(\\n    xlabel=\\\"Inverse rate (log10 words per appearance)\\\",\\n    ylabel=\\\"Density\\\",\\n)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -2241,19 +2397,30 @@
     }
    ],
    "source": [
-    "posterior.plot()"
+    "prior.plot(alpha=0.5, label=\"prior\")\n",
+    "posterior.plot(label=\"posterior\")\n",
+    "decorate(\n",
+    "    xlabel=\"Inverse rate (log10 words per appearance)\",\n",
+    "    ylabel=\"Density\",\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Make a Prediction"
+    "If you go 50 years without hearing a word, that suggests that it is a rare word, and the posterior distribution reflects that logic.\n",
+    "\n",
+    "The posterior distribution represents a range of possible values for the inverse rate of the word you heard.\n",
+    "Now we can use it to answer the question we started with: what is the probability of hearing the same word again on the same day -- that is, within the next 10,000 words you hear.\n",
+    "\n",
+    "To answer that, we can use the survival function of the binomial distribution to compute the probability of more than 0 successes in the next `n_pred` attempts.\n",
+    "We'll compute this probability for each of the `ps` that correspond to the inverse rates in the posterior."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 357,
+   "execution_count": 92,
    "metadata": {},
    "outputs": [
     {
@@ -2261,9 +2428,9 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 357;\n",
-       "                var nbb_unformatted_code = \"n_pred = words_per_day\\nps_pred = binom.sf(0, n_pred, ps)\";\n",
-       "                var nbb_formatted_code = \"n_pred = words_per_day\\nps_pred = binom.sf(0, n_pred, ps)\";\n",
+       "                var nbb_cell_id = 92;\n",
+       "                var nbb_unformatted_code = \"from scipy.stats import binom\\n\\nn_pred = words_per_day\\nps_pred = binom.sf(0, n_pred, ps)\";\n",
+       "                var nbb_formatted_code = \"from scipy.stats import binom\\n\\nn_pred = words_per_day\\nps_pred = binom.sf(0, n_pred, ps)\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
        "                for (var i = 0; i < nbb_cells.length; ++i) {\n",
        "                    if (nbb_cells[i].input_prompt_number == nbb_cell_id) {\n",
@@ -2285,22 +2452,31 @@
     }
    ],
    "source": [
+    "from scipy.stats import binom\n",
+    "\n",
     "n_pred = words_per_day\n",
     "ps_pred = binom.sf(0, n_pred, ps)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And we can use the probabilities in the posterior to compute the expected value."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 358,
+   "execution_count": 93,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "(0.00016066773432600893, 6224.0250302584855)"
+       "(0.00016010294670308533, 6245.981230155142)"
       ]
      },
-     "execution_count": 358,
+     "execution_count": 93,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -2309,7 +2485,7 @@
       "application/javascript": [
        "\n",
        "            setTimeout(function() {\n",
-       "                var nbb_cell_id = 358;\n",
+       "                var nbb_cell_id = 93;\n",
        "                var nbb_unformatted_code = \"p = np.sum(posterior * ps_pred)\\np, 1 / p\";\n",
        "                var nbb_formatted_code = \"p = np.sum(posterior * ps_pred)\\np, 1 / p\";\n",
        "                var nbb_cells = Jupyter.notebook.get_cells();\n",
@@ -2337,6 +2513,18 @@
     "p, 1 / p"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The chance of hearing the same word again within a day is about 1 in 6000.\n",
+    "With all of the assumptions we made in this calculation, there's no reason to be more precise than that.\n",
+    "\n",
+    "And as I mentioned at the beginning, we should probably not take this conclusion to seriously.\n",
+    "If you hear a word for the first time after 50 years, there's a good chance the word is \"having a moment\", which greatly increases the chance you'll hear it again.\n",
+    "I can't think of why chartism might be in the news at the moment, but maybe this post will go viral and make it happen."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},