What is the correlation of X and 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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![**Joint Probability Mass Function Table**
Consider the following joint random variable PMF (Probability Mass Function) for \(X\) and \(Y\):
\[
\begin{array}{|c|c|c|}
\hline
x & y & f_{XY}(x, y) \\
\hline
-1 & 0 & \frac{1}{4} \\
\hline
0 & 1 & \frac{1}{8} \\
\hline
1 & 1 & \frac{1}{2} \\
\hline
1 & 0 & \frac{1}{8} \\
\hline
\end{array}
\]
### Notation:
- \( x \) and \( y \) are the possible values that the random variables \( X \) and \( Y \) can take.
- \( f_{XY}(x, y) \) represents the joint probability mass function, which gives the probability that \( X = x \) and \( Y = y \) simultaneously.
### Table Explanation:
- When \( X = -1 \) and \( Y = 0 \), the probability \( f_{XY}(-1, 0) = \frac{1}{4} \).
- When \( X = 0 \) and \( Y = 1 \), the probability \( f_{XY}(0, 1) = \frac{1}{8} \).
- When \( X = 1 \) and \( Y = 1 \), the probability \( f_{XY}(1, 1) = \frac{1}{2} \).
- When \( X = 1 \) and \( Y = 0 \), the probability \( f_{XY}(1, 0) = \frac{1}{8} \).
### Question:
What is the correlation of \( X \) and \( Y \)?
---
The table defines the joint distribution of the variables \( X \) and \( Y \) and is used to calculate various statistical metrics, including their correlation. To find the correlation, you would need to determine the expected values \( E[X] \), \( E[Y] \), \( E[XY] \), the variances \( \sigma_X^2 \) and \( \sigma_Y^2 \), and then use the standard correlation formula:
\[ \text{Correlation}(X, Y) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fd71444-c22f-486e-ba4e-9500881f0dc0%2Fa9c4b130-2bf8-47a8-a825-60d758ad18b2%2F7vld4bd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Joint Probability Mass Function Table**
Consider the following joint random variable PMF (Probability Mass Function) for \(X\) and \(Y\):
\[
\begin{array}{|c|c|c|}
\hline
x & y & f_{XY}(x, y) \\
\hline
-1 & 0 & \frac{1}{4} \\
\hline
0 & 1 & \frac{1}{8} \\
\hline
1 & 1 & \frac{1}{2} \\
\hline
1 & 0 & \frac{1}{8} \\
\hline
\end{array}
\]
### Notation:
- \( x \) and \( y \) are the possible values that the random variables \( X \) and \( Y \) can take.
- \( f_{XY}(x, y) \) represents the joint probability mass function, which gives the probability that \( X = x \) and \( Y = y \) simultaneously.
### Table Explanation:
- When \( X = -1 \) and \( Y = 0 \), the probability \( f_{XY}(-1, 0) = \frac{1}{4} \).
- When \( X = 0 \) and \( Y = 1 \), the probability \( f_{XY}(0, 1) = \frac{1}{8} \).
- When \( X = 1 \) and \( Y = 1 \), the probability \( f_{XY}(1, 1) = \frac{1}{2} \).
- When \( X = 1 \) and \( Y = 0 \), the probability \( f_{XY}(1, 0) = \frac{1}{8} \).
### Question:
What is the correlation of \( X \) and \( Y \)?
---
The table defines the joint distribution of the variables \( X \) and \( Y \) and is used to calculate various statistical metrics, including their correlation. To find the correlation, you would need to determine the expected values \( E[X] \), \( E[Y] \), \( E[XY] \), the variances \( \sigma_X^2 \) and \( \sigma_Y^2 \), and then use the standard correlation formula:
\[ \text{Correlation}(X, Y) =
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