Repeat Problem 6.60 when X and Y are independent exponential random variables, each with parameter = 1. Problem 6.60 If X and Y are

Repeat Problem 6.60 when X and Y are independent exponential random variables, each with parameter λ = 1.

Problem 6.60

If X and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of

a. U = X + Y, V = X/Y;

b. U = X, V = X/Y;

c. U = X+ Y, V = X/(X + Y).