30. Let X₁, . . ., X_n be a set of independent and identically distributed continuous random variables having distribution function F, and let X₍₁₎ ≤ . . . ≤ X_(n)

denote their ordered values. If X, independent of the X_i, 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.