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).