The Joint Probability Distribution of X and Y Is Shown $$\begin{array} { c | c c c } & & X \\\hline Y&1& 2 & 3 \\\hline 1 & .30 & .18 & .12 \\2 & .15 & .09 & .06 \\3 & .05 & .03 & .02\end{array}$$

Essay

The joint probability distribution of X and Y is shown in the following table. $$\begin{array} { c | c c c } & & X \\\hline Y&1& 2 & 3 \\\hline 1 & .30 & .18 & .12 \\2 & .15 & .09 & .06 \\3 & .05 & .03 & .02\end{array}$$
a. Determine the marginal probability distributions of X and Y.
b. Are X and Y independent? Explain.
c. Find $P ( Y = 2 \mid X = 1 )$
d. Find the probability distribution of the random variable X+Y.
e. Find E(XY).
f. Find COV(X, Y).