3. Consider Simple Random Walk S₁ = 1X; on Z started at So = 0. Suppose that the X; are IID with P(X; = 1) = p and P(X; = − 1) = q = 1-p, for some p € (0,1). (a) What does the Law of Large Numbers tell us about Sn? Give both an informal and a more technique answer. (b) What does the Central Limit Theorem tell us about Sn? Give both an informal and a more technique answer.
3. Consider Simple Random Walk S₁ = 1X; on Z started at So = 0. Suppose that the X; are IID with P(X; = 1) = p and P(X; = − 1) = q = 1-p, for some p € (0,1). (a) What does the Law of Large Numbers tell us about Sn? Give both an informal and a more technique answer. (b) What does the Central Limit Theorem tell us about Sn? Give both an informal and a more technique answer.
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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Transcribed Image Text:3. Consider Simple Random Walk Sn = [1 X; on Z started at So= 0. Suppose
that the X; are IID with P(X; = 1) = p and P(X; = − 1) = q = 1 - p, for some
P€ (0,1).
(a) What does the Law of Large Numbers tell us about Sn? Give both an
informal and a more technique answer.
(b) What does the Central Limit Theorem tell us about S₁? Give both an
informal and a more technique answer.
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