Question

4. X and Y are random variables with a joint distribution given below: \begin{tabular}{c|ccc} & \multicolumn{3}{c}{$X = x$} \\ \cline{2-4} $Y = y$ & 0 & 2 & 4 \\ \hline 0 & 0.05 & 0.10 & 0.25 \\ 2 & 0.20 & 0.15 & 0.25 \\ \end{tabular} (a) Obtain the marginal distributions of X and Y. (4 marks) (b) Evaluate E(X), Var(X), E(Y) and Var(Y). (4 marks) (c) Obtain the conditional distributions of Y | X = 2 and X | Y = 2. (4 marks) (d) Evaluate E(XY), Cov(X, Y) and Corr(X, Y). (5 marks) (e) Are X and Y independent? Justify your answer. (3 marks)

          4. X and Y are random variables with a joint distribution given below:

\begin{tabular}{c|ccc}
 & \multicolumn{3}{c}{$X = x$} \\
\cline{2-4}
$Y = y$ & 0 & 2 & 4 \\
\hline
0 & 0.05 & 0.10 & 0.25 \\
2 & 0.20 & 0.15 & 0.25 \\
\end{tabular}

(a) Obtain the marginal distributions of X and Y.
(4 marks)
(b) Evaluate E(X), Var(X), E(Y) and Var(Y).
(4 marks)
(c) Obtain the conditional distributions of Y | X = 2 and X | Y = 2.
(4 marks)
(d) Evaluate E(XY), Cov(X, Y) and Corr(X, Y).
(5 marks)
(e) Are X and Y independent? Justify your answer.
(3 marks)

4. X and Y are random variables with a joint distribution given below:

3cX = x

2-4
Y = y 0 2 4

0 0.05 0.10 0.25

2 0.20 0.15 0.25

(a) Obtain the marginal distributions of X and Y.
(4 marks)
(b) Evaluate E(X), Var(X), E(Y) and Var(Y).
(4 marks)
(c) Obtain the conditional distributions of Y | X = 2 and X | Y = 2.
(4 marks)
(d) Evaluate E(XY), Cov(X, Y) and Corr(X, Y).
(5 marks)
(e) Are X and Y independent? Justify your answer.
(3 marks)

Added by David J.

Question

Please give Ace some feedback