1. The discrete random variables X and Y have known joint probability mass function [c x=0,1,2,L,9, y=0,1,2,L,9, yzx otherwise , where c = 1/55. 0 Pxy(x, y) given by Py(x, y) = Define the event B = {X² + y² ≤25}. a) Determine the conditional PMF P(x, y/B) of the random variables X and Y. b) Determine the conditional marginal PMFs P(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.)
1. The discrete random variables X and Y have known joint probability mass function [c x=0,1,2,L,9, y=0,1,2,L,9, yzx otherwise , where c = 1/55. 0 Pxy(x, y) given by Py(x, y) = Define the event B = {X² + y² ≤25}. a) Determine the conditional PMF P(x, y/B) of the random variables X and Y. b) Determine the conditional marginal PMFs P(x/B) and P(y/B) of the random variables X and Y. c) Determine the conditional correlation E{XY/B} of the random variables X and Y. (Take advantage of the solutions to Prob. 1 in Homework #8.)
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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![1. The discrete random variables \(X\) and \(Y\) have known joint probability mass function \( P_{XY}(x, y) \) given by
\[
P_{XY}(x, y) =
\begin{cases}
c & x = 0, 1, 2, L, \ 9, \ y = 0, 1, 2, L, \ 9, \ y \geq x \\
0 & \text{otherwise}
\end{cases}
\]
where \( c = 1/55 \).
Define the event \( B = \{ X^2 + Y^2 \leq 25 \} \).
a) Determine the conditional PMF \( P_{XY}(x, y / B) \) of the random variables \(X\) and \(Y\).
b) Determine the conditional marginal PMFs \( P_X(x / B) \) and \( P_Y(y / B) \) of the random variables \(X\) and \(Y\).
c) Determine the conditional correlation and \( E\{XY / B\} \) of the random variables \(X\) and \(Y\).
(Take advantage of the solutions to Prob. 1 in Homework #8.)
Solution for [Homework 8](#) is COV(\(X,Y\))=3, correlation = \(1/2\), not statistically independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9328926a-b343-4d47-8a00-cbd9e6e36ac2%2Fa146204c-d296-48e8-a901-20a73206106d%2Fel0yv2_processed.png&w=3840&q=75)
Transcribed Image Text:1. The discrete random variables \(X\) and \(Y\) have known joint probability mass function \( P_{XY}(x, y) \) given by
\[
P_{XY}(x, y) =
\begin{cases}
c & x = 0, 1, 2, L, \ 9, \ y = 0, 1, 2, L, \ 9, \ y \geq x \\
0 & \text{otherwise}
\end{cases}
\]
where \( c = 1/55 \).
Define the event \( B = \{ X^2 + Y^2 \leq 25 \} \).
a) Determine the conditional PMF \( P_{XY}(x, y / B) \) of the random variables \(X\) and \(Y\).
b) Determine the conditional marginal PMFs \( P_X(x / B) \) and \( P_Y(y / B) \) of the random variables \(X\) and \(Y\).
c) Determine the conditional correlation and \( E\{XY / B\} \) of the random variables \(X\) and \(Y\).
(Take advantage of the solutions to Prob. 1 in Homework #8.)
Solution for [Homework 8](#) is COV(\(X,Y\))=3, correlation = \(1/2\), not statistically independent.
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