Let X and Y be two random variables that are uniformly distributed over the triangle formed by the points (0, 0), (1. 0) , and (0, 2) (this is an asymmetric version of the PDF in the previous problem). Calculate E[X] and E[Y] by following the same steps as in the previous problem. (a) Find the joint PDF of X and Y .
(b) Find the marginal PDF of Y .
(c) Find the conditional PDF of X given Y .
(d) Find E[X|Y = y] and use the total expectation theorem to find E[X] in terms of E[Y ].
(e) Use the symmetry of the problem to find the value of E[X].