1. Refer to Exercise 12.
a. Let Z = X + Y represent the total number of repairs needed.
b. Find µZ .
c. Find σZ .
d. Find P(Z = 2).
2. Refer to Exercise 12. Assume that the cost of an engine repair is $50, and the cost of a transmission repair is $100. Let T represent the total cost of repairs during a one-hour time interval.
a. Find µT .
b. Find σT .
c. Find P(T = 250)
3. Refer to Exercise 12.
a. Find the conditional probability mass function pY|X (y | 3).
b. Find the conditional probability mass function pY|X (x | 1).
c. Find the conditional expectation E(Y | X = 3).
d. Find the conditional expectation E(X | Y = 1).