4. Let X₁, i = 1,2,..., be independent random variables with P(X₂ = 1) = ½, P(X₁ = − 1) = 1/2. PutFo= {2,0}, F₁ = 0(X₁, X2,..., Xn), n ≥ 1.Define So= 0, Sn =₁X₁, n ≥ 1.i) Show that Zn = S²-n, n ≥ 0 is a martingale with respect to {Fn, n ≥ 0}.

From the given information, Xi, i=1,2,.... be independent random variables with PXi=1=12, PXi=-1=12…

Answered: 4. Let X₁, i = 1, 2, ...., be…

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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4. Let X₁, i = 1, 2, ...., be independent random variables with P(X₁ = 1) = ½, P(X₁ = − 1) = 1/2. Put Fo= {2,0}, Fn = 0(X₁, X2,..., Xn), n ≥ 1.