(c) Let Y1 be a random variable with probability density function given by 6y1 (1 - y1), 0

(c) Let Yl be a random variable with probability density function given by 6911 (1 Yl), 0 1, f(Yl) - 0, elsewhere, and let Y2 be a random variable with probability density function given by g(Y2) - 0, elsewhere. Consider the transformation U = YIY2. If Yl and Y2 are independent, find the proba- bility density function for U. 6 pts