Exercise 13. Let X₁,..., Xn~ N(x, 0²) i.i.d. and Y₁,..., Yn ~ N(µy, 02) i.i.d. with known o².We assume that for each i the random variables X; and Y; are correlated, with Corr(Xį, Y₁) = 1/2.Define D₁ = X₁ - Yį for all i = {1,...,n}. Finally, let X, Y and D be the averages of the Xi, Yiand Di, respectively.a) Show that Cov(X₁, Yi) = 0²/2.b) Determine E(D₁) and Var(D₁).c) Consider the test for Ho: x = µy which uses the test statisticZ = √√nDσand which rejects Ho, if and only if |Z| > 1.96. Show that P(type I error) = 5%.d) In two or three sentences, discuss the differences between the test from part (c) on the onehand, and the non-paired test for comparing the means of two populations on the otherhand.

The provided information is as follows: and are i.i.d variables.

Answered: Exercise 13. Let X₁,..., Xn~ N(a,02)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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