3. (20 points) A production facility contains two machines that are used to rework items that are initially defective. Let 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 f(x,y) = ={{< *) +y) 0< x,y <1 0 otherwise a. (3 points) Find the marginal PDF of X. b. (3 points) Find the marginal PDF of Y. c. 17 points) Find the conditional probability density function frix (y1 0.5). d. 17 points) Find the conditional expectation EY | X = 0.5).