Question: Let X and Y be independent random variables with the same geometric distribution. (a) Show that U and V are independent, where U and V

Let X and Y be independent random variables with the same geometric distribution.
(a) Show that U and V are independent, where U and V are defined by
U = min(X, Y) and V = X - Y,
(b) Find the distribution of Z = X/(X + Y), where we define Z = 0 if X + Y = 0.
(c) Find the joint pdf of X and X + Y.

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a The support of the distribution of U V is u v u 1 2 v 012 If V 0 then X Y So for v 1 2 the joint p... View full answer

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