Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Unfortunately, not everyone survives long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We assume X Y and model time to death as X Exp(rate = ) and time to transplant as Y Exp(rate = ). Where Exp(rate = ) denotes the exponential distribution with density f(z | ) = ez for z > 0 and 0 elsewhere - with > 0. a. (5 points) Express the probability that a patient receives transplant before death in probability/random variable notation. b. (10 points) What is the joint density fXY (x, y)? Show that it is a valid density. c. (15 points) Compute the probability in part (a) by integrating over the joint density from (b).