# Eleisha's Segment 13: The Yeast Genome

To Calculate:

1. With p=0.3, and various values of n, how big is the largest discrepancy between the Binomial probability pdf and the approximating Normal pdf? At what value of n does this value become smaller than $\displaystyle 10^{-15}$ ?

2. Show that if four random variables are (together) multinomially distributed, each separately is binomially distributed.

1. The segment suggests that $\displaystyle A\ne T$ and $\displaystyle C\ne G$ comes about because genes are randomly distributed on one strand or the other. Could you use the observed discrepancies to estimate, even roughly, the number of genes in the yeast genome? If so, how? If not, why not?
2. Suppose that a Bayesian thinks that the prior probability of the hypothesis that "$\displaystyle P_A=P_T$ " is 0.9, and that the set of all hypotheses that "$\displaystyle P_A\ne P_T$ " have a total prior of 0.1. How might he calculate the odds ratio $\displaystyle \text{Prob}(P_A=P_T)/\text{Prob}(P_A\ne P_T)$ ? Hint: Are there nuisance variables to be marginalized over?