# Discussion1.pdf - Discussion 1 Jan 30, 2021 Hector Zheng...

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Discussion 1Hector Zheng ([email protected])Jan 30, 2021
About the discussion sessionTwo identical discussion sessions will be held every week.Discussion Section 1:Friday, 1:00 - 1:59 PMDiscussion Section 2:Friday, 2:00 - 2:59 PMYou may attend either of the two sessions as you wish.All discussion sessions will be recorded.Week 1, 3, 5, … will be held by meWeek 2, 4, 6, … will be held by Jingxu
AgendaWe’ll go through three problems today.For each problem, we will pause for three minutes foryou to think about it.Not being able tofinish or having no idea is okay.The problems are not for testing but to help you betterunderstand the concepts taught in formal lectures.
Problem 1An individual traveling on the real line is trying to reach the origin. However, the larger thestep desired, the greater is the variance in the result of that step. Specifically, whenever theperson is at location, he next moves to a location having meanand variance. Letdenote the position of the individual after having takensteps. Supposing that,a deterministic value. Find1.2.x0βx2XnnX0=x0x0E[Xn]Var(Xn)is
Solution to Problem 11.(given)2.E[Xn]= 0Var(Xn)=E[X2n](E[Xn])2=E[X2n](using part 1)=E[E[X2nXn1]]=E[βX2n1]=βE[X2n1]E[X2n]=βE[X2n1]=β2E[X2n2]

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Term
Winter
Professor
NoProfessor
Tags
Probability theory, Markov chain, Andrey Markov, Coin