3. Let X and Y be discrete random variables with the following joint probability function. X Y f(x,y) = P(X=x,Y=y) 2 4 0.15 2 7 0.25 11 4 0.32 7 0.28 E 11 (a) Is the above a valid PMF? Verify (b) Using the table above find the expected value of X, E[X]. (c) Using the table above find the expected value of Y, E[Y]. (d) Using the table above find the expected value of XY, E[XY]. (e) Determine the covariance of XY, note Cov(X,Y)= E[XY] − E[X] * E[Y].
3. Let X and Y be discrete random variables with the following joint probability function. X Y f(x,y) = P(X=x,Y=y) 2 4 0.15 2 7 0.25 11 4 0.32 7 0.28 E 11 (a) Is the above a valid PMF? Verify (b) Using the table above find the expected value of X, E[X]. (c) Using the table above find the expected value of Y, E[Y]. (d) Using the table above find the expected value of XY, E[XY]. (e) Determine the covariance of XY, note Cov(X,Y)= E[XY] − E[X] * E[Y].
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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Hi. I only need help for questions d) and e) please.
![### Probability and Statistics: Joint Probability Distribution
**Problem 3:**
Let \(X\) and \(Y\) be discrete random variables with the following joint probability function.
\[
\begin{array}{ccc}
\text{X} & \text{Y} & f(x, y) = P(X=x, Y=y) \\
\hline
2 & 4 & 0.15 \\
2 & 7 & 0.25 \\
11 & 4 & 0.32 \\
11 & 7 & 0.28 \\
\end{array}
\]
**Questions:**
(a) Is the above a valid PMF? Verify.
(b) Using the table above, find the expected value of \(X\), \(E[X]\).
(c) Using the table above, find the expected value of \(Y\), \(E[Y]\).
(d) Using the table above, find the expected value of \(XY\), \(E[XY]\).
(e) Determine the covariance of \(XY\). Note \( \text{Cov}(X, Y) = E[XY] - E[X] \times E[Y] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8b48535-184f-4977-af2d-d816dbce40fd%2Fa25273a6-0ed6-4745-a36f-9228b964b980%2Ftj2uoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics: Joint Probability Distribution
**Problem 3:**
Let \(X\) and \(Y\) be discrete random variables with the following joint probability function.
\[
\begin{array}{ccc}
\text{X} & \text{Y} & f(x, y) = P(X=x, Y=y) \\
\hline
2 & 4 & 0.15 \\
2 & 7 & 0.25 \\
11 & 4 & 0.32 \\
11 & 7 & 0.28 \\
\end{array}
\]
**Questions:**
(a) Is the above a valid PMF? Verify.
(b) Using the table above, find the expected value of \(X\), \(E[X]\).
(c) Using the table above, find the expected value of \(Y\), \(E[Y]\).
(d) Using the table above, find the expected value of \(XY\), \(E[XY]\).
(e) Determine the covariance of \(XY\). Note \( \text{Cov}(X, Y) = E[XY] - E[X] \times E[Y] \).
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