Question: Let Ui,i = 1,2,..., be independent uniform(0,1) random variables, and let X have distribution P(X = x) = c/x x = l, 2,3,..., X where

Let Ui,i = 1,2,..., be independent uniform(0,1) random variables, and let X have distribution P(X = x) = c/x x = l, 2,3,..., X
where c = l/(e - 1). Find the distribution of
Z = min{U1,... ,Ux}.
(That the distribution of Z|X = x is that of the first-order statistic from a sample of size x.)

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