Lecture 2: Probability and population genetics

Question 1

Difference between random variable and realisation

Answer 1

A random variable has a list of outcomes. When an experiment has been performed and the variable taken a value this is termed a realisation.

Question 2

What is a probability distribution?

Answer 2

Function that assigns a probability for a subset of outcomes for a random variable.

Question 3

Name the most important discrete distributions

Answer 3

Bernulli
Binomial
Poisson

Question 4

Name the most important continuous distributions:

Answer 4

The normal distribution
Exponential
chi-square
beta

Question 5

Marginal density function

Answer 5

It is the a sub-density function. e.g. look only at the whole y distribution.

Question 6

Conditional density function

Answer 6

keep at at certain value and look at the other distribution at that value.

Question 7

What is independence?

Answer 7

If knowledge of X gives no information of Y.

F_{Y| X=x}(y) = F_Y(y)

Which gives:

F_{X,Y)(x,y) = F_X(x)*f_Y(y)

Question 8

Covariance:

Answer 8

Expected value of the product of realisation minus expectation.

Question 9

Independence implies

Answer 9

Uncorrelatedness

Question 10

What is allele frequency estimation?

Answer 10

Estimation of the proportion of chromosomes that carry a specific allele.

can be done using number of people with genotype AA, Aa and aa (nAA, nAa and, naa respectively. Proportion of A is then:

p = (2nAA 0 nAa)/2n

a freq is 1-p

Question 11

Variance of allele estimation:

Answer 11

The chromosomes in a sample can be thought of as independent. This means that the amount of alleles is binomially distributed with:

p = X (number of alleles) / 2n

2np ~ Binom(2n,p)

V(p) = p(1-p)/2n