After watching a number of children playing games is a video arcade, a statistics practitioner estimated the following probability distribution of X, the number of games per visit.

X: __ F(x):

1 __ 0.05

2 __ 0.15

3 __ 0.15

4 __ 0.25

5 __ 0.20

6 __ 0.10

7 __ 0.10

a. What is the probability that child will play at least two games?

b. What is the mean and variance of the number of games played?

c. Suppose that each game costs $0.25. Use the laws of expected value and variance to

determine the expected value and variance of the amount of money the arcade takes

in per child.

d. Determine the probability distribution of the amount of money the arcade takes in per

child.

e. Use the probability distribution to calculate the mean and variance of the amount of

money the arcade takes in per child.

f. Are your answers in part c & part e identical?