Examples

Covariance from PMF chart

Suppose the joint PMF of and is given by this chart:

	0.2	0.2
	0.35	0.1
	0.05	0.1

Find .

Solution

We need and and .

Therefore:

Variance of sum of indicators

An urn contains 3 red balls and 2 yellow balls.

Suppose 2 balls are drawn without replacement, and counts the number of red balls drawn.

Find .

Solution

Let indicate (one or zero) whether the first ball is red, and indicate whether the second ball is red, so .

Then indicates whether both drawn balls are red; so it is Bernoulli with success probability . Therefore .

We also have .

The variance sum rule gives: