Question 8. Random variables \( X \) and \( Y \) have the joint PMF
\[
P_{X, Y}(x, y)=\left\{\begin{array}{ll}
c x y, & x=1,2,4, y=1,3, \\
0, & \text { otherwise. }
\end{array}\right.
\]
(a) What is the value of the constant \( c \) ?
(b) What is \( P(Y<X) \) ?
(c) What is \( P(Y>X) \) ?
(d) What is \( P(Y=X) \) ?
(c) Find the marginal PMFs \( P_{X}(x) \) and \( P_{Y}(y) \).
(f) Find the expected values \( E(X) \) and \( E(Y) \).
(g) Find the standard deviations \( \sigma_{X} \) and \( \sigma_{Y} \).