Let (Y1, Y2) have joint density function fY1,Y2 (y1, y2) and let U1 = Y1 Y2 and U2 = Y2. Find the joint density function of (U1, U2). Hint: Your answer will be in function notation. fU1,U2 (u1, u2) =

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297