Finding E(Y) and Var(Y) with Conditional Expectation

[island-boy]

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?

 

[0rthodontist]

No it is not. Let Y be distributed as f(x) = .5 if x = -1 or 1, 0 otherwise. Let X be distributed as f(x) = 1 if x = 1, 0 otherwise. Then f(Y|X) is the distribution of X. You can change the mean and variance of Y to almost whatever you want by moving the other probability mass, and f(Y|X) will not be affected.