Question: Let U1, U2,..., Un be i.i.d. Unif(0, 1) random variables. Let X = min(U1, U2,..., Un) and Y = max(U1, U2, ..., Un) Fx(x)

Let U1, U2,..., Un be i.i.d. Unif(0, 1) random variables. Let X

Let U1, U2,..., Un be i.i.d. Unif(0, 1) random variables. Let X = min(U1, U2,..., Un) and Y = max(U1, U2, ..., Un) Fx(x) = 1 (1 x)" the marginal cdfs of X and Y are Fy(y) = xn The joint cdf of X and Y is given by P(X x, y y) = y" (y x)", 0 x y 1 (a) Find the density of R = Y-X. (b) Show that R is a biased estimator of the range of Unif(0, 1).

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