A random variable X has a probabilitydistributionasXP(X) = D6aCp(x) 1/4 1/2 1/4]It is correlated with the other random variable Y(0,1).Their relation can beX\Y1/2 1/22/3 1/31/4 3/41adescribed by conditional probability matrix P(Y/X) =b%3D 1) calculate its entropy, H(X).2) calculate P(Y) and entropy of Y, H(Y).3) calculate the joint and conditional entropy H(XY) and H(Y/X).4) calculate the mutual information I(X,Y).5) calculate the conditional entropy H(X/Y).

Given probability distribution of random variable of X is PX=Xabcpx141214 and conditional…

A random variable X has a probability distribution as X a b C P(X) = |p(x) 1/4 1/2 1/4] It is correlated with the other random variable Y(0,1). Their relation can be |X\Y 1 1/2 1/2 a described by conditional probability matrix P(Y/X) = b 2/3 1/3 1/4 3/4

A random variable X has a probability distribution as X a b C P(X) = |p(x) 1/4 1/2 1/4] It is correlated with the other random variable Y(0,1). Their relation can be |X\Y 1 1/2 1/2 a described by conditional probability matrix P(Y/X) = b 2/3 1/3 1/4 3/4

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

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Question

A random variable X has a probability
distribution
as
X
P(X) = D6
a
C
p(x) 1/4 1/2 1/4]
It is correlated with the other random variable Y(0,1).
Their relation can be
X\Y
1/2 1/2
2/3 1/3
1/4 3/4
1
a
described by conditional probability matrix P(Y/X) =
b
%3D

1) calculate its entropy, H(X).
2) calculate P(Y) and entropy of Y, H(Y).
3) calculate the joint and conditional entropy H(XY) and H(Y/X).
4) calculate the mutual information I(X,Y).
5) calculate the conditional entropy H(X/Y).

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