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).

Question

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).

Quizplus · Accepted Answer

The Answer of 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).

The Joint Probability Distribution of X and Y Is Shown XY1231.30.18.122.15.09.063.05.03.02\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}Y123​1.30.15.05​X2.18.09.03​3.12.06.02​​

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