Question

Let X and Y be two random variables such that X is uniform over the interval (0,1) and, given X = x, Y is uniform over the interval (0, x + 1).

(i) Find the joint pdf f(x,y) of X and Y and specify it support (i.e., the set of the pairs (x,y) such that f(x,y) > 0.)
(ii) Find E(Y |X = x).
(iii) Find the marginal pdf fY (y) of Y and specify its support.

Answer 1