Let X, Y be independent exponential random variables with means 1 and 2 respectively.
Let
Z = 1, if X < Y
Z = 0, otherwise
Find E(X|Z) and V(X|Z).
We should first find E(X|Z=z)
E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
However, how do we find f(x|z) ?