Suppose that, for some N, the continuous random variables X₁, X2,..., XN are independently drawn from the uniform distribution on [-1,1]. That is, each X₂ Uniform([-1,1]). Let S = X₁ + X2 + ... + XN denote the sum of these uniform random variables. The Central Limit Theorem allows us to approximate the true sum Sy as a Gaussian random variable we'll call G. (It is up to you to find the mean and variance of G.) Notice that since each X; is bounded, Sy is also bounded. In particular, the true sum Sy can only take values between -N and N. However, the Gaussian approximation to Sy is not bounded: G has some small probability of taking values greater than N (or less than -N). Find an expression for P(|G| > N). Your answer should be in terms of N, and it should involve the Gaussian cdf function Þ(.). Hint: for large values of N, P(|G| > N) goes to 0.

Suppose that, for some N, the continuous random variables X₁, X2,..., XN are independently drawn from the uniform distribution on [-1,1]. That is, each X₂ Uniform([-1,1]). Let S = X₁ + X2 + ... + XN denote the sum of these uniform random variables. The Central Limit Theorem allows us to approximate the true sum Sy as a Gaussian random variable we'll call G. (It is up to you to find the mean and variance of G.) Notice that since each X; is bounded, Sy is also bounded. In particular, the true sum Sy can only take values between -N and N. However, the Gaussian approximation to Sy is not bounded: G has some small probability of taking values greater than N (or less than -N). Find an expression for P(|G| > N). Your answer should be in terms of N, and it should involve the Gaussian cdf function Þ(.). Hint: for large values of N, P(|G| > N) goes to 0.

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...

See similar textbooks