The joint density function for X and Y is f(x,y) = { e^-y, 0 < x < y < ? 0, e.w a. Prove that f(x,y) is a pdf. b. Show that X and Y are dependent random variables. c. Find E(XY) d. Find P(0 < X < 0.5|Y=1) e. Find E(X|Y=y)
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Prove that f(x,y) is a pdf: To prove that f(x,y) is a pdf, we need to show that it satisfies two conditions: a) f(x,y) >= 0 for all (x,y) in the sample space. This is clearly satisfied as a is a constant and x < y < 0, so f(x,y) = a >= 0. b) The integral of Show more…
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