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, y≥x otherwise where c is a Pxy(x, y) given by Py(x, y) = constant. a) Determine the value of the constant c that makes the above Pxy(x, y) a valid joint probability mass function. b) Determine the marginal probability mass functions Px(x) and Py(y). Are the random variables statistically independent? c) Determine the covariance cov(X,Y) of the random variables X and Y. d) Determine the correlation coefficient Px of the random variables X and Y c) Is the expected value E{XY} equal to E{X}E{Y}? Explain why it is or why it is not. 3
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, y≥x otherwise where c is a Pxy(x, y) given by Py(x, y) = constant. a) Determine the value of the constant c that makes the above Pxy(x, y) a valid joint probability mass function. b) Determine the marginal probability mass functions Px(x) and Py(y). Are the random variables statistically independent? c) Determine the covariance cov(X,Y) of the random variables X and Y. d) Determine the correlation coefficient Px of the random variables X and Y c) Is the expected value E{XY} equal to E{X}E{Y}? Explain why it is or why it is not. 3
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
\[
P_{XY}(x, y) =
\begin{cases}
c & x = 0, 1, 2, \ldots, 9, \; y = 0, 1, 2, \ldots, 9, \; y \geq x \\
0 & \text{otherwise}
\end{cases}
\]
where \( c \) is a constant.
a) Determine the value of the constant \( c \) that makes the above \( P_{XY}(x, y) \) a valid joint probability mass function.
b) Determine the marginal probability mass functions \( P_X(x) \) and \( P_Y(y) \). Are the random variables statistically independent?
c) Determine the covariance \( \text{cov}(X, Y) \) of the random variables \( X \) and \( Y \).
d) Determine the correlation coefficient \( \rho_{XY} \) of the random variables \( X \) and \( Y \).
c) Is the expected value \( E\{XY\} \) equal to \( E\{X\}E\{Y\} \)? Explain why it is or why it is not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9328926a-b343-4d47-8a00-cbd9e6e36ac2%2F633aa604-1bf5-4d46-9098-d528e8d30d5d%2Fmphz5gf_processed.jpeg&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
\[
P_{XY}(x, y) =
\begin{cases}
c & x = 0, 1, 2, \ldots, 9, \; y = 0, 1, 2, \ldots, 9, \; y \geq x \\
0 & \text{otherwise}
\end{cases}
\]
where \( c \) is a constant.
a) Determine the value of the constant \( c \) that makes the above \( P_{XY}(x, y) \) a valid joint probability mass function.
b) Determine the marginal probability mass functions \( P_X(x) \) and \( P_Y(y) \). Are the random variables statistically independent?
c) Determine the covariance \( \text{cov}(X, Y) \) of the random variables \( X \) and \( Y \).
d) Determine the correlation coefficient \( \rho_{XY} \) of the random variables \( X \) and \( Y \).
c) Is the expected value \( E\{XY\} \) equal to \( E\{X\}E\{Y\} \)? Explain why it is or why it is not.
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VIEWStep 2: Determine value of constant c that makes the above PXY(x,y) a valid joint probability mass function.
VIEWStep 3: Determine the marginal probability mass functions Px(x) and Py(y).
VIEWStep 4: Determine the covariance cov(X,Y) of the random variables X and Y.
VIEWStep 5: Determine the correlation coefficient of the random variable X and Y.
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