Let X be the number of people in a household for a certain community. Consider the following probability density for X, which assumes that there are no more than severn people in the household:

Value of X

X = x {1, 2, 3, 4, 5, 6, 7}

Probability

P(X = x) {0.20, 0.32, 0.18, 0.15, 0.07, 0.03}

a. What must be the probability of seven people in a household for this to be a legitimate discrete density?

b. What is the probability that a randomly chosen household contains more than five people?

c. What is the probability that a randomly chosen household contains no more than two people?

d. What is P(2 < X =<4)?

e. What is the expected number of people in a household?

f. Find the variance for the number of people per household.

g. If you randomly select a household from those containing at least 3 people, what is the probability you will select a household that has 7 people?