I don't have a clue how to work this one out. The solution I've seen doesn't make sense to me... Can anyone explain this in detail?

X & Y have a joint distribution with pdf f(x,y) = exp^-(x+y), x>0 , y>0.

The random variable Z is defined to be equal to U = exp^-(x+y).

Find the pdf of U, f(u).

Answer is f(u) = -ln u for 0<u<1

Thanks for the help!

X & Y have a joint distribution with pdf f(x,y) = exp^-(x+y), x>0 , y>0.

The random variable Z is defined to be equal to U = exp^-(x+y).

Find the pdf of U, f(u).

Answer is f(u) = -ln u for 0<u<1

Thanks for the help!

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