b) Let X₁, X₂, X and Y₁, Y₂... Y be random samples from populations with moment generating25functions Mx, (t) = e3t+t² and My, (t) =respectively.i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X4 + X5.ii) What is the value of the sample size n, if P[Σ(X-X)² > 68.3392] = 0.025?iii) What is the value of the sample size m, if P(|Y-ul> 10) <0.04? b) Let X₁, X₂, X and Y₁, Y₂... Y be random samples from populations with moment generating25functions Mx, (t) = e3t+t² and My, (t) =respectively.i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X4 + X5.ii) What is the value of the sample size n, if P[Σ(X-X)² > 68.3392] = 0.025?iii) What is the value of the sample size m, if P(|Y-ul> 10) <0.04?

Solution: From the given information, the moment generating functions of X and Y are

Answered: Let X₁, X₂,..., X and Y₁, Y2...., Ym be…

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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a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR 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 rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
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