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:

a. Find the marginal probability mass function pX (x).

b. Find the marginal probability mass function pY (y).

c. Find μ_X.

d. Find μ_Y.

e. Find σ_X.

f. Find σ_Y.

g. Find Cov(X, Y).

h. Find ρ_X,Y.

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y 2 3 х 0.13 0.10 0.07 0.03 0.12 0.16 0.08 0.04 2 0.02 0.01 0.06 0.08 0.04 3 0.02 0.02 0.02