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.

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...
icon
Related questions
Question
4. Let X₁, i = 1,2,..., be independent random variables with P(X₂ = 1) = ½, P(X₁ = − 1) = 1/2. Put
Fo= {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}.
Transcribed Image Text:4. Let X₁, i = 1,2,..., be independent random variables with P(X₂ = 1) = ½, P(X₁ = − 1) = 1/2. Put Fo= {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}.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON