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

Question: Let X1, . . . ,Xn be a set of independent and identically distributed continuous random variables having distribution function F, and let X(i), i

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