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

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Question

Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X~N(0,1)
and Y =
-√n.
√n
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.
iv) What is the probability that Y² is between 0.02 and 5.02?

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