Given the joint density where . What is the best way to find ?
1) Integrate the joint distribution with respect to y. E.g. in order to find the marginal distribution of X. Then apply But the above integration is hard to solve.
2) Using conditional probability method. First find the conditional distribution of X given Y=y e.g and solve for E(X) with E[E(X|Y)]=E[X]. I've got this but what about finding ?
3) Use the fact that with Finding is quite tedious which require to solve for Moreover, I have no idea how to obtain though I know that [tex]E(X|Y)=y[/tex] which is