Question: Suppose that X and Y are i.i.d. random variables, and that each has the following p.d.f.: Also, let U = X/(X + Y) and V

Suppose that X and Y are i.i.d. random variables, and that each has the following p.d.f.:

Suppose that X and Y are i.i.d. random variables, and

Also, let U = X/(X + Y) and V = X + Y.
a. Determine the joint p.d.f. of U and V.
b. Are U and V independent?

e for 0, 0 otherwise f(x)=

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