Question

A group of five people are randomly selected from an office of five men and nine women. The random variable X denotes the number of women in the group selected.

What is the probability mass function and expected value of X?

Answer 1

Given:

A group of five people are randomly selected from an office of five men and nine women.

Number of sample = n = 5

k = 9, m = 5

N = 5+9 = 14

The random variable X denotes the number of women in the group selected.

Here X follows the Hypergeometric distribution with parameters n = 5, N = 14 , k = 9

X ~ Hypergeometric (N=14, k=9, n=5)

The probability mass function of hypergeometric distribution is given by

Therefore the expected value of X is E(X) = 3.21