Suppose that Xt is a Poisson Process with parameter λ = 1. Find E(X1 | X2) and E(X2 | X1).
I think they should be equal but I'm not sure how to write the value of the expectation of either.
Can you calculate the conditional distribution for P(X1=x|X2=y) and find its expectation?
You also have to tell us what kind of expectation you want to find since it is a multi-dimensional random variable: the expectation can be any general function of X1 and X2 or E[f(X1,X2)] and if you don't specify this then it won't make sense.