1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## Find the conditional probability mass function pY|X (y | 3).

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).