Suppose that X and Y have a joint probability density function (pdf)
f(x; y) =
k(x + 2y) for 0 < x < 1 and 0 < y < 1;
0 otherwise.
(a) Find k such that f(x; y) is indeed a valid pdf.
(b) Find the marginal pdf of Y .
(c) Find E(Y ).
(d) Find the conditional pdf fXjY (x j y).
(e) Find P(X 0:5 j Y = 0:5).