A production facility contains two machines that are used to rework items that are initially defective. LetXbe the number of hours that the first machine is in use, and letYbe the number of hours that the second machine is in use, on a randomly chosen day. Assume thatXandYhavejoint probability density function given bya. What is the probability that both machines are in operation for more than half an hour?
b. Find the marginal probability density functions fX(x) and fY(y).
c. Are X and Y independent? Explain.