Homework Help is Here – Start Your Trial Now!
Math
Statistics
.) Using the joint density directly, find E[X₁ — X₂]. i.) Using the joint density directly, find E[X₁ X₂], and the Cov(X₁, X2).

.) Using the joint density directly, find E[X₁ — X₂]. i.) Using the joint density directly, find E[X₁ X₂], and the Cov(X₁, X2).

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

Solve parts 10 and 11 

Thanks

Q1 Let (X₁, X₂) be jointly continuous with joint probability density function 0 < x2 < x1 < 1, otherwise. f(x1, x₂) = x1 0 Q1(i.) Sketch(Shade) the support of (X₁, X₂). Q1(ii.) Find the marginal density function of X₁. Q1(iii.) Find the marginal density function of X₂. Q1(iv.) Find E[X₁]. Q1(v.) Find E[X₂]. Q1(vi.) Find the conditional density of X₂ given X₁ = x₁, i.e., fx₂x₁ (x₂|x₁). Q1(vii.) Find the conditional expectation of X₂ given X₁ x₁, i.e. E[X₂|X₁ = x₁]. = Q1(viii.) What is E[X₂X₁]? Using the property of conditional expectation, verify that E[X₂] is the same as the one obtained in part Q1(v.). Q1(ix.) Using the joint density directly, find E[X₂] and verify that it is the same as obtained Q1(v.) and Q1(viii.). Q1(x.) Using the joint density directly, find E[X₁ — X₂]. Q1(xi.) Using the joint density directly, find E[X₁ X₂], and the Cov(X₁, X₂).
Transcribed Image Text:Q1 Let (X₁, X₂) be jointly continuous with joint probability density function 0 < x2 < x1 < 1, otherwise. f(x1, x₂) = x1 0 Q1(i.) Sketch(Shade) the support of (X₁, X₂). Q1(ii.) Find the marginal density function of X₁. Q1(iii.) Find the marginal density function of X₂. Q1(iv.) Find E[X₁]. Q1(v.) Find E[X₂]. Q1(vi.) Find the conditional density of X₂ given X₁ = x₁, i.e., fx₂x₁ (x₂|x₁). Q1(vii.) Find the conditional expectation of X₂ given X₁ x₁, i.e. E[X₂|X₁ = x₁]. = Q1(viii.) What is E[X₂X₁]? Using the property of conditional expectation, verify that E[X₂] is the same as the one obtained in part Q1(v.). Q1(ix.) Using the joint density directly, find E[X₂] and verify that it is the same as obtained Q1(v.) and Q1(viii.). Q1(x.) Using the joint density directly, find E[X₁ — X₂]. Q1(xi.) Using the joint density directly, find E[X₁ X₂], and the Cov(X₁, X₂).
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