# Question

Let X1, . . . ,Xn be a set of independent and identically distributed continuous random variables having distribution function F, and let X(i), i = 1, . . . , n denote their ordered values. If X, independent of the Xi, i = 1, . . . , n, also has distribution F, determine

(a) P{X > X(n)};

(b) P{X > X(1)};

(c) P{X(i) < X < X(j)}, 1 ≤ i < j ≤ n.

(a) P{X > X(n)};

(b) P{X > X(1)};

(c) P{X(i) < X < X(j)}, 1 ≤ i < j ≤ n.

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