Typos correction and suggestions

[mtomasini]

With the Bradburd Lab at MSU, we read the first part of your amazing notes, so well done! Thank you!
We're glad to help fixing some typos we noticed. We also have a couple of suggestions (unfortunately Makrdown on Github does not support equations, but I leave them in markdown notation). These notes were provided by @bobweek:

• pg 31, eqn (2.11), suggestion: use $F_{A_i}$ instead of $f_{A_i}$ since $f$ used to denote genotype frequencies.

• pg 43, eqn (3.7): confusing notation.

  • what is $\mathrm{Var}(p_1,\dots,p_K)$?
  • $\bar p$ is not a random variable, so what is $\mathrm{Var}(\bar p)$?
  • suggestion: set $X_i\sim\mathrm{Bin}(p_i)$ and $X\sim\mathrm{Bin}(\bar p)$, then $F_{ST}=\frac{\overline{\mathrm{Var}(X_i)}}{\mathrm{Var}(X)}.$

• pg 44, eqn (3.8): confusing/informal way of writing a probability. Would be more clear to write the probability of an event, e.g., the probability of the event $g_l=0$ given pop $=k$ would be written
  $$\mathbb{P}(g_l=0 \ | \ \mathrm{pop}=k)=(1-p_{kl})^2.$$

• pg 44, eqn (3.9): following the above comment, in my notes i wrote $g=(g_1,\dots,g_S)$ as the unkown genotype and $\gamma=(\gamma_1,\dots,\gamma_S)$ as an instance so that the probability of an individual with a particular genotype, given pop $=k$ is
  $$\mathbb{P}(g=\gamma \ | \ \mathrm{pop}=k)=\prod_{l=1}^S\mathbb{P}(g_l=\gamma_l \ | \ \mathrm{pop}=k).$$