Question: Let U, U, M(x) = M(y) dy + 1, x1 x> 1 be independent uniform (0, 1) random variables, and let N denote the smallest

Let U, U, M(x) = M(y) dy + 1, x1 x> 1 be independent uniform (0, 1) random variables, and let N denote the smallest value of n, n 0, such that n+1 0 where U, 1 Show that N is a Poisson random variable with mean A (Hint. Show by induction on n, conditioning on U, that P{N = n} = e-^\"/n!)

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