Using the joint probability table below, determine E(XY). 4357 101 0.05 0.05 0.15 0.3 0.15 0 0.15 0.1 0.05
Using the joint probability table below, determine E(XY). 4357 101 0.05 0.05 0.15 0.3 0.15 0 0.15 0.1 0.05
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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please solve.
![**Problem Statement:**
Using the joint probability table below, determine \( E(XY) \).
**Joint Probability Table:**
\[
\begin{array}{c|c|c|c}
Y\backslash X & -1 & 0 & 1 \\
\hline
3 & 0.05 & 0.05 & 0.15 \\
5 & 0.15 & 0.3 & 0.1 \\
7 & 0.15 & 0 & 0.05 \\
\end{array}
\]
**Explanation:**
This table provides the joint probabilities \( P(X = x, Y = y) \) for different values of random variables \( X \) and \( Y \).
- The first row indicates the possible values of \( X \): -1, 0, and 1.
- The first column (excluding the label) indicates the possible values of \( Y \): 3, 5, and 7.
- Each cell in the table contains the probability associated with a specific pair \((X = x, Y = y)\).
**Objective:**
Calculate the expectation \( E(XY) \) using the formula:
\[
E(XY) = \sum_{x}\sum_{y} x \cdot y \cdot P(X = x, Y = y)
\]
This involves multiplying each possible \( x \) and \( y \) pair by its respective probability, then summing all these products to obtain \( E(XY) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5a46a21-656d-42a0-a455-81d241d5836d%2F1ad7ca74-5145-40a1-8d8e-f364decb731d%2Fs9br8hj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Using the joint probability table below, determine \( E(XY) \).
**Joint Probability Table:**
\[
\begin{array}{c|c|c|c}
Y\backslash X & -1 & 0 & 1 \\
\hline
3 & 0.05 & 0.05 & 0.15 \\
5 & 0.15 & 0.3 & 0.1 \\
7 & 0.15 & 0 & 0.05 \\
\end{array}
\]
**Explanation:**
This table provides the joint probabilities \( P(X = x, Y = y) \) for different values of random variables \( X \) and \( Y \).
- The first row indicates the possible values of \( X \): -1, 0, and 1.
- The first column (excluding the label) indicates the possible values of \( Y \): 3, 5, and 7.
- Each cell in the table contains the probability associated with a specific pair \((X = x, Y = y)\).
**Objective:**
Calculate the expectation \( E(XY) \) using the formula:
\[
E(XY) = \sum_{x}\sum_{y} x \cdot y \cdot P(X = x, Y = y)
\]
This involves multiplying each possible \( x \) and \( y \) pair by its respective probability, then summing all these products to obtain \( E(XY) \).
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