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...

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. LetXrepresent the number of engines, andYthe number of transmissions that require repairs in a one-hour time interval. The joint probability mass function ofXandYis as follows:

Find Cov(X, Y).

Find ρ_X,Y .

Extracted text: 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: y 0.10 0.16 0.06 0.02 0.13 0.07 0.08 0.08 0.02 0.03 1 0.12 0.04 0.02 0.04 3 0.01 0.02