Repeat Problem 1 when X and Y are independent exponential random variables, each with parameter λ = 1.
Problem 1
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, Y= X /( X + Y ).
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