Chapter 2.6, Problem 15E

Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows:

15.    Refer to Exercise 12.

1. a. Find the conditional probability mass function p_Y|X (y | 3).
2. b. Find the conditional probability mass function p_X|Y (x | 1).
3. c. Find the conditional expectation E(Y | X = 3).
4. d. Find the conditional expectation E(X | Y = 1).

1. a. Find the marginal probability mass function p_X (x).
2. b. Find the marginal probability mass function p_Y (y).
3. c. Find μ_X.
4. d. Find μ_Y.
5. e. Find σ_X.
6. f. Find σ_Y.
7. g. Find Cov(X, Y).
8. h. Find ρ_{X, Y}.