A production facility contains two machines that are used to rework items that are initially defective. Let 8. A x be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by x2 y 2) 0 x 1 and 0 y 1 f(x) otherwise a. What is the probability that both machines are in operation for more than half an hour? b. Find the marginal probability density functions f (r) and fr (y). c. Are X and Y independent? Explain.