The data set below details a random variable x is the number of houses sold by a realtor in a single month at the Strano Real Estate office.Show your work to receive partial Houses Sold (x)

0

1

2

3

4

5

6

7

Probability P(x)

0.24

0.18

0.16

0.15

0.12

0.09

0.04

0.02

21.A. Given the data set above, determine if it is a valid probability distribution. If it is not valid, explain why.If it is, find the mean and variance of the given probability distribution.

21.B.What is the expected value for this probability distribution?Note: if the distribution is not a valid probability distribution, you can respond "Not Applicable."

21.C.What is the probability that the realtor will sell 5 or more houses in one month.

21.D. Would it be considered "unusual" if the realtor sold 0 houses in one month?Why or why not?