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 pmf of X and X + Y.

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A: Hello! As you have posted 4 sub parts, we are answering the first 3 sub-parts.  In case you require…

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