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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