What is the covariance for the joint distribution below right? Cov(X, Y) = -1 YO +1 -1 1/16 3/16 1/16 X 0 3/16 0 3/16 +1 1/16 3/16 1/16
What is the covariance for the joint distribution below right? Cov(X, Y) = -1 YO +1 -1 1/16 3/16 1/16 X 0 3/16 0 3/16 +1 1/16 3/16 1/16
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![**Question:**
What is the covariance for the joint distribution below right?
**Joint Distribution Table:**
\[
\begin{array}{c|c|c|c}
& X = -1 & X = 0 & X = +1 \\
\hline
Y = -1 & \frac{1}{16} & \frac{3}{16} & \frac{1}{16} \\
\hline
Y = 0 & \frac{3}{16} & 0 & \frac{3}{16} \\
\hline
Y = +1 & \frac{1}{16} & \frac{3}{16} & \frac{1}{16} \\
\end{array}
\]
**Explanation:**
- The table represents a joint distribution for two random variables \(X\) and \(Y\).
- Each cell in the table indicates the joint probability \(P(X, Y)\) for specific values of \(X\) and \(Y\).
- The rows correspond to the values of \(Y\) (-1, 0, +1), and the columns correspond to the values of \(X\) (-1, 0, +1).
- The probabilities \(P(X = i, Y = j)\) for each combination of \(i\) and \(j\) are provided as fractions of 16.
The task is to calculate the covariance \( \text{Cov}(X, Y) \) using this joint distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd53b5d21-36fa-4ee2-932f-fd40dc0982c5%2Fc34e90ef-fb16-451e-9269-1f05f8550d11%2Fi9hwbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the covariance for the joint distribution below right?
**Joint Distribution Table:**
\[
\begin{array}{c|c|c|c}
& X = -1 & X = 0 & X = +1 \\
\hline
Y = -1 & \frac{1}{16} & \frac{3}{16} & \frac{1}{16} \\
\hline
Y = 0 & \frac{3}{16} & 0 & \frac{3}{16} \\
\hline
Y = +1 & \frac{1}{16} & \frac{3}{16} & \frac{1}{16} \\
\end{array}
\]
**Explanation:**
- The table represents a joint distribution for two random variables \(X\) and \(Y\).
- Each cell in the table indicates the joint probability \(P(X, Y)\) for specific values of \(X\) and \(Y\).
- The rows correspond to the values of \(Y\) (-1, 0, +1), and the columns correspond to the values of \(X\) (-1, 0, +1).
- The probabilities \(P(X = i, Y = j)\) for each combination of \(i\) and \(j\) are provided as fractions of 16.
The task is to calculate the covariance \( \text{Cov}(X, Y) \) using this joint distribution.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 9 images
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON