Any hints on how to solve for E(Y|X) given the ff:
Suppose U and V are independent with exponential distributions
f(t) = \lambda \exp^{-\lambda t}, \mbox{ for } t\geq 0
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...
Is it possible to solve for E(Y) and var (Y) when I am only given the distribution f(Y|X)?
I can solve for E(Y|X). But is it possible to find E(Y) and var(Y) given only this info?