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Ehrenfest model of diffusion. We have a total of n balls,

Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis ISBN: 9781886529236 227

Solution for problem 15 Chapter 7

Introduction to Probability, | 2nd Edition

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Introduction to Probability, | 2nd Edition | ISBN: 9781886529236 | Authors: Dimitri P. Bertsekas John N. Tsitsiklis

Introduction to Probability, | 2nd Edition

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15
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Problem 15

Ehrenfest model of diffusion. We have a total of n balls, some of them black, some white. At each time step, we either do nothing, which happens with probability f, where 0 < f < 1, or we select a ball at random, so that each ball has probability (1 - f ) / n > 0 of being selected. In the latter case, we change the color of the selected ball (if white it becomes black, and vice versa), and the process is repeated indefinitely. What is the steady-state distribution of the number of white balls?

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Lecture 11 Nicole Rubenstein October 10, 2017 Contents 1 Continuous random variables 1 1.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1. . . . . . . . 2 Properties 2 3 Probability density function 2 3.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 . . . . . . . . 3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . 4 Quantile

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Chapter 7, Problem 15 is Solved
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Textbook: Introduction to Probability,
Edition: 2
Author: Dimitri P. Bertsekas John N. Tsitsiklis
ISBN: 9781886529236

This textbook survival guide was created for the textbook: Introduction to Probability,, edition: 2. The full step-by-step solution to problem: 15 from chapter: 7 was answered by , our top Statistics solution expert on 01/09/18, 07:43PM. Since the solution to 15 from 7 chapter was answered, more than 248 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 326 solutions. Introduction to Probability, was written by and is associated to the ISBN: 9781886529236. The answer to “Ehrenfest model of diffusion. We have a total of n balls, some of them black, some white. At each time step, we either do nothing, which happens with probability f, where 0 < f < 1, or we select a ball at random, so that each ball has probability (1 - f ) / n > 0 of being selected. In the latter case, we change the color of the selected ball (if white it becomes black, and vice versa), and the process is repeated indefinitely. What is the steady-state distribution of the number of white balls?” is broken down into a number of easy to follow steps, and 97 words.

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Ehrenfest model of diffusion. We have a total of n balls,