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(a) Show that Sn/√n has mean 0 and standard deviation 1. (b) Using the Central Limit Theorem, show there is about a 12% that the distance from the origin after 100 steps exceeds 15. show that P(|S100 | > 15) ≈ 12%.

(a) Show that Sn/√n has mean 0 and standard deviation 1. (b) Using the Central Limit Theorem, show there is about a 12% that the distance from the origin after 100 steps exceeds 15. show that P(|S100 | > 15) ≈ 12%.

A First Course in Probability (10th Edition)
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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:1 . Consider symmetric (p = 1/2) Simple Random Walk on the integers Z. Recall that the position of the walk after n steps is Sn = So +₁ X₁, where the X; are independent and identically distributed, with each P(X; = ±1) = 1/2. Suppose that the walk is started at the origin, So = 0.
Transcribed Image Text::1 . Consider symmetric (p = 1/2) Simple Random Walk on the integers Z. Recall that the position of the walk after n steps is Sn = So +₁ X₁, where the X; are independent and identically distributed, with each P(X; = ±1) = 1/2. Suppose that the walk is started at the origin, So = 0.
(a) Show that Sn/√n has mean 0 and standard deviation 1. (b) Using the Central Limit Theorem, show there is about a 12% that the distance from the origin after 100 steps exceeds 15. show that P(|S100] > 15) ≈ 12%. Note: Be sure to use a "discrete adjustment",
Transcribed Image Text:(a) Show that Sn/√n has mean 0 and standard deviation 1. (b) Using the Central Limit Theorem, show there is about a 12% that the distance from the origin after 100 steps exceeds 15. show that P(|S100] > 15) ≈ 12%. Note: Be sure to use a "discrete adjustment",
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