Let the random variable X and Y have the joint pmf
$\qquad f(x, y) = \frac{x^2 y^2}{c}, x = 1, 2; y = 1, 2, 3$
and c > 0.
a. Find c.
b. Find $\mu_x$.
c. Find $\mu_y$.
d. Find $\sigma_x^2$.
e. Find $\sigma_y^2$.
f. Find Cov(X, Y).
g. Find $\rho$, Corr(X, Y).
h. Are X and Y independent?
i. Find Var(X|Y = 2).