Question

Find the variance of the random variable in Exercise 54 of Chapter Four.

54. A committee is to consist of 50 randomly chosen United States senators. Find the expected number of different states to be represented on the committee.

Answer 1

Answer:

we can do this easily using indicator variables

define the indicator variable Xi = 1 if the ith state is represented,
and 0 otherwise
by linearity of expectation we have
E(# of states represented) = E?(Xi) = ?E(Xi)

the expectation of an indicator random variable is just the probability of the event it indicates,
and P(Xi) = 1 - P(ith state not represented)
= 1 - P(neither senator selected) = 1 - 98c50/100C50

thus E(# of states represented )
= ?E(Xi) = 50*(1 - 98c50/100c50) = 37.62626