A family will have children until they have one of each gend

A family will have children until they have one of each gender or will stop at 5 children. Let X be the number of children in a family.

1. determine the probability density function of X

2. Determine the expected value of X.

3. Determine the variance of X.

a) geometric distribution

b) expected value of X : 1/2 * 5 = 2.5

c) var = 1/2 * 1/2 * 5 = 1.25