1. A continuous random variable, say X, has the uniform distribution function on (0, 1)

so that the p.d.f. of X is given by f(x) =

⎧⎨

⎩

0, x≤ 0 1, 0 < x ≤ 1 0, x>1 If X(1),X(2), . . . , X(n) are the order statistics of n independent observations all having this distribution function, give the expression for the density g(x) for

(a) The largest of these n observations.

(b) The smallest of these n observations.

(c) The rth smallest of these n observations.