1. Two numbers are seleeted at random from te interval (0, I ). If these values are uniformly and independently distributed, compute the prob­ ability that the three resulting line segments, by cutting the interval at the numbers, can form a triangle.

2. Let X and Y denote independent random variables with respec­ tive probability density functions f(x) = 2x, 0 <>x <>I , zero elsewhere, and g(y) = 3y2, 0 <>y <>I , zero elsewhere. Let U = min (X, Y) and V = max (X, Y). Find the joint p.d .f. of U and V.

Hint: Here the two inverse transformations are given by x = u, y = v and x = v, y = u.