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4. For a Uniform [0, 1] distribution, recall that the order statistics, X(1) = min{X1, X2} and X(2) = max {X1, X2}, have densities f(x)

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4. For a Uniform [0, 1] distribution, recall that the order statistics, X(1) = min{X1, X2} and X(2) = max {X1, X2}, have densities f(x) = 2 -2x for the min and f(x) = 2x for the max (both supported on [0, 1]). Now suppose that X1 and X2 are independent draws from Uniform [a, b]. (a) For a = 0 and b = 1, i.e. the Uniform[0, 1] distribution, calculate E(X(1) ) and E(X(2)). (b) Now let a

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