# Segment 13. The Yeast Genome

## Contents

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

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Links to the slides: PDF file or PowerPoint file

Link to the file mentioned in the segment: SacSerChr4.txt

Link to all yeast chromosomes: UCSC

### Problems

#### 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 $10^{-15}$?

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

1. The segment suggests that $A\ne T$ and $C\ne G$ 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 "$P_A=P_T$" is 0.9, and that the set of all hypotheses that "$P_A\ne P_T$" have a total prior of 0.1. How might he calculate the odds ratio $\text{Prob}(P_A=P_T)/\text{Prob}(P_A\ne P_T)$? Hint: Are there nuisance variables to be marginalized over?

### Class Activity

For what range of X can the null hypothesis be rejected with p<____ in a ____-sided test distributed as ____? Individual contests for these versions of the question:

• Normal, p<5%, 2-sided (answer: X<-1.96 or X>1.96)
• Student, nu=4, p<5%, 2-sided (answer: X<-2.77 or X>2.77)
• Student, nu=2, p<1%, 1-sided (answer: X > 6.9646)
• Exponential, mu=2.7, p<0.001, 1-sided (answer: X>18.6509)
• same as above, but 2-sided (answer: 0<X<0.0014 or X>20.5224)
• F-distribution, nu1=6, nu2=8, p<0.1%, 1-sided (answer: X>12.85)
• Binomial, N=20, pbin=0.333, p<2%, 2-sided (answer: 0,1,12,13,...,20)
• same as above, but use Normal approximation (answer: X<1.75 or X>11.56)
• $p(x) = \frac{2}{\pi}\left(\frac{\sin x}{x}\right)^2$, p<0.01, 1-sided (answer: X>32.3138)