Q.6.18 Suppose X and Y are both integer... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

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 is $\frac{P (X = i, Y = j)}{\underset{i}{鈭�} \frac{P (X = i, Y = j)}{P (Y = j, X = i)}} = \frac{p (i / j)}{\underset{i}{鈭�} \frac{p (i, j)}{q (j, i)}}$

Step by step solution

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.

Content Explanation

We have

$P (X = i, Y = j) = \frac{P (X = i, Y = j)}{1} = \frac{P (X = i, Y = j)}{\underset{i}{鈭�} P (X = i)} = \frac{P (X = i, Y = j)}{\underset{i}{鈭�} \frac{P (X = i)}{P (Y = j)} . P (Y = j)} = \frac{P (X = i, Y = j)}{\underset{i}{鈭�} \frac{P (X = i, Y = j)}{P (Y = j, X = i)}} = \frac{p (i / j)}{\underset{i}{鈭�} \frac{p (i, j)}{q (j, i)}}$

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91影视

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

Step by step solution

Content Introduction

Content Explanation

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91影视

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

Step by step solution

Content Introduction

Content Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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