Any hints on how to solve for E(Y|X) given the ff:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose U and V are independent with exponential distributions

[tex]f(t) = \lambda \exp^{-\lambda t}, \mbox{ for } t\geq 0[/tex]

Where X = U + V and Y = UV.

I am having difficulty finding f(Y|X)...

Also, solving for f(X,Y), I am also having difficulty transforming U and V to X and Y. I was able to define U and V to X and Y, but the terms are so complicated that its difficult to get the Jacobian.

So maybe, there's no need for transformation?

Help please. Thanks!

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# Conditional expectation (w/ transformation)

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