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Refer back to the Ehrenfest chain model described in Exercise 2 with $m=3$ balls. The possiblestates of the chain $X_{n}=$ number of balls in the left chamber after the $n$ th exchange are $\{0,1,2,3\}$$$\begin{array}{l}{\text { (a) Suppose that all four possible initial states are equally likely. Determine the probability }} \\ {\text { distributions of } X_{1} \text { and } X_{2} \text { . }}\end{array}$$$$\begin{array}{l}{\text { (b) Suppose instead that each of the three balls is initially equally likely to be placed in the left }} \\ {\text { or right chamber. In this situation, what is the initial distribution of the chain? }}\end{array}$$$$\begin{array}{l}{\text { (c) Using the initial distribution specified in (b), determine the unconditional distributions of } X_{1}} \\ {\text { and } X_{2} \text { . What do you notice? }}\end{array}$$

Intro Stats / AP Statistics

Chapter 6

Markov Chains

Section 3

Specifying an Initial Distribution

Probability Topics

Temple University

Missouri State University

University of North Carolina at Chapel Hill

Piedmont College

Lectures

0:00

04:36

Refer back to Exercise $2 …

06:59

Refer back to the Ehrenfes…

01:48

Four balls, each with mass…

05:18

Each the balls shown below…

01:32

Selecting Numbered Balls F…

05:52

Each of 2$N$ electrons (ma…

03:22

Multiple-Concept Example 3…

05:50

Show that if $M=\left(S, I…

05:27

Refer back to Exercise 1 i…

In Fig. $21-39,$ two tiny …

07:01

Consider a Markov chain wi…

03:06

Draw a diagram to represen…

What is the expected numbe…

05:48

(a) Count the number of el…

03:31

Nine numbered balls are dr…

03:11

Consider just four of the …

04:46

Probability Distribution A…

02:34

Consider a single-electron…

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