Suppose that: (a) Let V = XY . Find the joint pdf for (X, V )....

Question

Question

Suppose that:

$f(x,y) = xe^{-x(y+1)}, 0 < x < \infty , 0 < y < \infty$

(a) Let V = XY . Find the joint pdf for (X, V ). Use it to get the pdf for V .

(b) What is the conditional pdf for X, given V = v? What does this say about the relationship between X and V ?

(c) Show that Z = X + Y has pdf $f_{z}(z) = \int_{0}^{z}xe^{-x(z-x+1)}dx$ (Do not try to simplify it.)

Answer 1

Answer #1

Na (x, y 2x. De (onditien

Answer 2

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