(a) Mn+1=1+(1-2/M)μn. (b) Use (a) to prove that M Pa = 7/7+ Mn 2 2 M (M7²)" (EIXO) - 4/1) 2
(a) Mn+1=1+(1-2/M)μn. (b) Use (a) to prove that M Pa = 7/7+ Mn 2 2 M (M7²)" (EIXO) - 4/1) 2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow
ideas from gpt, but please do not believe its answer.Very very grateful!
![54. Consider the Ehrenfest urn model in which M molecules are distributed be-
tween two urns, and at each time point one of the molecules is chosen at
random and is then removed from its urn and placed in the other one. Let
Xn denote the number of molecules in urn 1 after the nth switch and let
Mn = E[X₂]. Show that
(a) Mn+1=1+ (1 – 2/Μ)μη·
(b) Use (a) to prove that
Mn =
n
M
4/1 + (M = ²)" (E[Xo] - M1)
쓸)
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2256d724-c606-4366-9dc1-f1aca4b67a6e%2F357387ac-b047-4b65-a378-019d69813c94%2F2f096zm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:54. Consider the Ehrenfest urn model in which M molecules are distributed be-
tween two urns, and at each time point one of the molecules is chosen at
random and is then removed from its urn and placed in the other one. Let
Xn denote the number of molecules in urn 1 after the nth switch and let
Mn = E[X₂]. Show that
(a) Mn+1=1+ (1 – 2/Μ)μη·
(b) Use (a) to prove that
Mn =
n
M
4/1 + (M = ²)" (E[Xo] - M1)
쓸)
2
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