The random variables X and have joint probability distribution specified by the following table: y=0 y=1 y=2 x=1 o Please provide all answers to the following to three decimal places. (a) Find the expectation of XY. 0.375 (b) Find the covariance Cov(X, Y) between X and Y. 64 (c) What is the correlation between X and Y? -0.0463 (d) Suppose the random variables X and Y above are connected to random variables U and V by the relations X = 9U + 9 Y = 4V + 8 What is the covariance Cov(U, V)? 5184 (e) What is the correlation between U and V?
The random variables X and have joint probability distribution specified by the following table: y=0 y=1 y=2 x=1 o Please provide all answers to the following to three decimal places. (a) Find the expectation of XY. 0.375 (b) Find the covariance Cov(X, Y) between X and Y. 64 (c) What is the correlation between X and Y? -0.0463 (d) Suppose the random variables X and Y above are connected to random variables U and V by the relations X = 9U + 9 Y = 4V + 8 What is the covariance Cov(U, V)? 5184 (e) What is the correlation between U and V?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The random variables \(X\) and \(Y\) have a joint probability distribution specified by the following table:
\[
\begin{array}{c|ccc}
& y=0 & y=1 & y=2 \\
\hline
x=0 & \frac{1}{4} & 0 & \frac{1}{8} \\
x=1 & \frac{1}{4} & \frac{3}{8} & 0 \\
\end{array}
\]
Please provide all answers to the following to three decimal places.
(a) Find the expectation of \(XY\).
\[
0.375
\]
(b) Find the covariance \(\text{Cov}(X, Y)\) between \(X\) and \(Y\).
\[
-\frac{1}{64}
\]
(c) What is the correlation between \(X\) and \(Y\)?
\[
-0.0463
\]
(d) Suppose the random variables \(X\) and \(Y\) above are connected to random variables \(U\) and \(V\) by the relations:
\[
X = 9U + 9
\]
\[
Y = 4V + 8
\]
What is the covariance \(\text{Cov}(U, V)\)?
\[
-\frac{1}{5184}
\]
(e) What is the correlation between \(U\) and \(V\)?
\[
\boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0d396c-e5f5-46c2-813a-9ed0820c37ca%2F90f8bf0c-e7ad-4146-8e62-29d832758685%2Fwisly7s_processed.png&w=3840&q=75)
Transcribed Image Text:The random variables \(X\) and \(Y\) have a joint probability distribution specified by the following table:
\[
\begin{array}{c|ccc}
& y=0 & y=1 & y=2 \\
\hline
x=0 & \frac{1}{4} & 0 & \frac{1}{8} \\
x=1 & \frac{1}{4} & \frac{3}{8} & 0 \\
\end{array}
\]
Please provide all answers to the following to three decimal places.
(a) Find the expectation of \(XY\).
\[
0.375
\]
(b) Find the covariance \(\text{Cov}(X, Y)\) between \(X\) and \(Y\).
\[
-\frac{1}{64}
\]
(c) What is the correlation between \(X\) and \(Y\)?
\[
-0.0463
\]
(d) Suppose the random variables \(X\) and \(Y\) above are connected to random variables \(U\) and \(V\) by the relations:
\[
X = 9U + 9
\]
\[
Y = 4V + 8
\]
What is the covariance \(\text{Cov}(U, V)\)?
\[
-\frac{1}{5184}
\]
(e) What is the correlation between \(U\) and \(V\)?
\[
\boxed{}
\]
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