Let X₁, X₂, X3,..., Xn be a random sample of size n from population X. Suppose that X~N(0, 1)=1 X-√n.√nand Y =i) Show that the standard score of the sample mean X, is equal to Y.ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively.iii) Show using the moment generating function technique that Y is a standard normal randomvariable.

It is given that X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

Answered: i) Show that the standard score of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal random variable.