Let X₁, X₂,... be independent random variables, each taking a value of either 1 (withprobability p) or -1 (with probability q = 1 − p). Assume So = a for some a € Z andletSn is known as the simple random walk. Show that:(i) Sn is spatially homogenous:(ii) Sn is temporally homogenous:Sn = a + X₁ for n ≥ 1.Note: |ai-ai-1|(iii) Sn has the Markov property:=nP(Sn = b|So = a) = P(Sn = b + c|So = a + c).i=1P(Sn = b|So = a) = P(Sm+n = b|Sm = a).P(Sm+nb|So ao, S₁ = a₁,..., Sm=am) = P(Sm+n=b|Sm= am).=1 for 1 < i

Given:Let be independent random variables, each taking a value of either 1 (with probability p) or…

Answered: Let X₁, X₂,... be independent random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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