Homework Help is Here – Start Your Trial Now!
Math
Statistics
Exercise 13. Let X₁,..., Xn~ N(x, o2) i.i.d. and Y1₁,..., Yn~ N(My, 02) i.i.d. with known o². We assume that for each i the random variables X, and Y₂ are correlated, with Corr(X₁, Y₁) = 1/2. Define D₁ = X₁ - Yį for all i € {1,...,n}. Finally, let X, Y and D be the averages of the X₁, Yi and Di, respectively. a) Show that Cov(Xi, Yi) = 02/2.

Exercise 13. Let X₁,..., Xn~ N(x, o2) i.i.d. and Y1₁,..., Yn~ N(My, 02) i.i.d. with known o². We assume that for each i the random variables X, and Y₂ are correlated, with Corr(X₁, Y₁) = 1/2. Define D₁ = X₁ - Yį for all i € {1,...,n}. Finally, let X, Y and D be the averages of the X₁, Yi and Di, respectively. a) Show that Cov(Xi, Yi) = 02/2.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Could you help me with c and d please .Could you also please provide written out explanations , not typed up please if possible

Exercise 13. Let X₁,..., Xn~ N(μx, 0²) i.i.d. and Y₁,..., Yn ~ N(μy, o²) i.i.d. with known o². We assume that for each i the random variables X; and Y; are correlated, with Corr(Xį, Yį) = 1/2. Define D₁ = X₁ - Yį for all i € {1,...,n}. Finally, let X, Ỹ and Ď be the averages of the Xį, Yi and Di, respectively. a) Show that Cov(X₁, Yi) = 0²/2. b) Determine E(D₁) and Var(D₂). c) Consider the test for Ho: μx = µy which uses the test statistic Z = √n O and 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 one hand, and the non-paired test for comparing the means of two populations on the other hand.
Transcribed Image Text:Exercise 13. Let X₁,..., Xn~ N(μx, 0²) i.i.d. and Y₁,..., Yn ~ N(μy, o²) i.i.d. with known o². We assume that for each i the random variables X; and Y; are correlated, with Corr(Xį, Yį) = 1/2. Define D₁ = X₁ - Yį for all i € {1,...,n}. Finally, let X, Ỹ and Ď be the averages of the Xį, Yi and Di, respectively. a) Show that Cov(X₁, Yi) = 0²/2. b) Determine E(D₁) and Var(D₂). c) Consider the test for Ho: μx = µy which uses the test statistic Z = √n O and 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 one hand, and the non-paired test for comparing the means of two populations on the other hand.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS