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chapter15.html
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<h1 class="title toc-ignore">Chapter 15</h1>
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<li><a href="#random-variables"><span class="toc-section-number">1</span> Random variables</a></li>
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<div id="random-variables" class="section level1">
<h1><span class="header-section-number">1</span> Random variables</h1>
<p>For making probability models, we can use Variance and Standard deviation just as before.</p>
<p>Think about an insurance company that pays out £10,000 if you die; £5,000 if you get disabled, and nothing if you are OK.</p>
<p>Every year, 1 person dies, 2 people get disables and 997 people are OK and don’t receive any payout.</p>
<p>The mean is therefore (10,000 x 1 + 5,000 x 2 + 0 x 997) / 1,000 = £20 payout per person.</p>
<pre class="r"><code>mean = ((10000 * 1) + (5000 * 2) + (997 *0))/1000
mean</code></pre>
<pre><code>## [1] 20</code></pre>
<p>The total payout per year is the mean multipled by the number of people = 20 * 1000 = £20,000.</p>
<p>Arrive at the same values if we take each individual outcome and probability of that outcome e.g.</p>
<p>£10,000 * 1/1000 + £5,0000 * 2/1000 + £0 * 997/1000 = £20</p>
<p>mean = sum xP(x)</p>
<p><span class="math inline">\(\sigma\)</span></p>
<p>The variance of X is the same as saying the sum of all x - mean squared, multipled by the Probability of X.</p>
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