Question: Let X and Y be independent random variables with X ~ gamma(r, 1) and Y ~ gamma(s, 1). Show that Z1 = X + Y

Let X and Y be independent random variables with X ~ gamma(r, 1) and Y ~ gamma(s, 1). Show that Z1 = X + Y and Z2 = X/(X + Y) are independent, and find the distribution of each. (Z1 is gamma and Z2 is beta.)

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