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Chapter 6: Q.6.18 (page 276)

Suppose X and Y are both integer-valued random variables. Let p(i|j) = P(X = i|Y = j) and q(j|i) = P(Y = j|X = i) Show that P(X = i, Y = j) = p(i|j)  i p(i|j) q(j|i

Short Answer

Expert verified

The required expression isP(X=i,Y=j)鈭�iP(X=i,Y=j)P(Y=j,X=i)=p(i/j)鈭�ip(i,j)q(j,i)

Step by step solution

01

Content Introduction

A random variable is a variable that has a set of possible values and probability. It's a variable whose value is determined by the outcome of an unknown event.

02

Content Explanation

We have

P(X=i,Y=j)=P(X=i,Y=j)1=P(X=i,Y=j)鈭�iP(X=i)=P(X=i,Y=j)鈭�iP(X=i)P(Y=j).P(Y=j)=P(X=i,Y=j)鈭�iP(X=i,Y=j)P(Y=j,X=i)=p(i/j)鈭�ip(i,j)q(j,i)

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