Question

Let (X,Y) have joint density f(x,y) -2x for0 <x < 1,0sys1 and 0 elsewhere. (a) Find P(xY > z) for 0szs1. Your final answer should be a function of z. (Hint: if you pick up a particular z, say,武what is the area within the unit square of 0 x 1 and 0 y 1 such that xy > z? P1.68 shows what you need to do, i.e., a double integral. Note thatz is a constant from the perspective of both x and y.) (b) Find the cumulative distribution function of the random variable Z - XY. Your final answer should be a function of z. (Hint: what's the definition of CDF? Can you leverage the result of (a) to figure out the CDF?) (c) Find EZ. Your final answer should be a number. (Hint: now that you have the CDF, figure out the PDF, and then follow P2.7.)

Answer 1