r+y, 0

1. Consider two continuous RVs X, Y with joint PDF fx,y (:r, y) Note that (X, Y) jointly take values inside the unit square. (a) (1 point) Verify that y) is a legitimate joint PDF. (I.e., verify it is non-negative and integrates to 1.) (b) (4 points) Find E(X). (Hint: Use the marginal distribution of X.) (c) (4 points) Find Var(X). (d) (6 points) Find Cov(X, Y). {0 otherwise (Hint: Due to the symmetry of the joint density, i.e., y) == x), VT, y, the marginal distribution of Y is the same as that of X, which implies that the mean and variance of Y are equal to those of X.) (e) (2 points) Find + Y). (f) (3 points) Find Var(X -4- Y).