:1. Consider symmetric (p = 1/2) Simple Random Walk on the integers Z. Recallthat 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",

Given that the position of the walk after n steps is Sn=S0+∑i=1nXi where S0=0 and Xi are…

Answered: (a) Show that Sn/√n has mean 0 and…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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(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%.