# Question

Let X(i), i = 1, . . . , n, denote the order statistics from a set of n uniform (0, 1) random variables, and note that the density function of X(i) is given by

f(x) = n!/(i − 1)!(n − i)! xi−1(1 − x)n−i 0 < x < 1

(a) Compute Var(X(i)), i = 1, . . . , n.

(b) Which value of i minimizes, and which value maximizes, Var(X(i))?

f(x) = n!/(i − 1)!(n − i)! xi−1(1 − x)n−i 0 < x < 1

(a) Compute Var(X(i)), i = 1, . . . , n.

(b) Which value of i minimizes, and which value maximizes, Var(X(i))?

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