Suppose that X and Y are independent and identically distrib

Suppose that X and Y are independent and identically distributed random variables with common pdf

Solution

U = x+y

V = x/x+y

As x and y are independent

f(x,y) = f(x)f(y) = e^-(x+y)

X=UV and Y = U-UV

J = V U

   1-V -U   

= -UV-U+uv =-1

Thus joint distribution of u,v

is -1 f(x,y)

Hence u and v are independent.