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the ways to come back in 2n steps) (bonus) Show that -o (2)² = (²n). Use the previous results to show that the walk is recurren We now consider the uniform random walk on Z³, whic ad and run the notebook for week 3, also available at this the number of visits in (0,0,0). Report the values obtain e probability of return P(X; = 0 for some i >0|Xo = 0).

the ways to come back in 2n steps) (bonus) Show that -o (2)² = (²n). Use the previous results to show that the walk is recurren We now consider the uniform random walk on Z³, whic ad and run the notebook for week 3, also available at this the number of visits in (0,0,0). Report the values obtain e probability of return P(X; = 0 for some i >0|Xo = 0).

MATLAB: An Introduction with Applications
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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Problem 2 (Random walk in Z² and Z³) a We consider the uniform random walk on Z². Show that the probability to return at the starting place after 2n steps is given by p2n = 42 (2) Σko (2)². (hint: use multinomial coefficient to count all the ways to come back in 2n steps) b (bonus) Show that Σo (2)² = (²n). c Use the previous results to show that the walk is recurrent. d We now consider the uniform random walk on Z³, which is transient (as mentioned in class). Read and run the notebook for week 3, also available at this link, to obtain an empirical histogram of the number of visits in (0, 0, 0). Report the values obtained and use them to get an estimate of the probability of return P(X; = 0 for some i > 0|Xo = 0).
Transcribed Image Text:Problem 2 (Random walk in Z² and Z³) a We consider the uniform random walk on Z². Show that the probability to return at the starting place after 2n steps is given by p2n = 42 (2) Σko (2)². (hint: use multinomial coefficient to count all the ways to come back in 2n steps) b (bonus) Show that Σo (2)² = (²n). c Use the previous results to show that the walk is recurrent. d We now consider the uniform random walk on Z³, which is transient (as mentioned in class). Read and run the notebook for week 3, also available at this link, to obtain an empirical histogram of the number of visits in (0, 0, 0). Report the values obtained and use them to get an estimate of the probability of return P(X; = 0 for some i > 0|Xo = 0).
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