f(x1, x₂) = x1 0 < x2 < x₁ < 1, otherwise. 21(i.) Sketch(Shade) the support of (X₁, X2). 21(ii.) Find the marginal density function of X₁. 21(iii.) Find the marginal density function of X₂. 21(iv.) Find E[X₁]. 21(v.) Find E[X₂]. 21(vi.) Find the conditional density of X₂ given X₁ = ₁, i.e., fx₂|X₁ (x2|x₁). 21(vii.) Find the conditional expectation of X₂ given X₁ = x₁, i.e. E[X₂|X₁ = x₁]. 21(viii.) What is E[X2|X₁]? Using the property of conditional expectation, verify that E[X₂] is the same as the one obtained in part 21 (v.). 21(ix.) Using the joint density directly, find E[X₂] and verify that it is the same as obtained Q1(v.) and Q1 (viii.). 21(x.) Using the joint density directly, find E[X₁ - X₂]. 21(xi.) Using the joint density directly, find E[X₁ X₂], and the Cov(X1, X₂).
f(x1, x₂) = x1 0 < x2 < x₁ < 1, otherwise. 21(i.) Sketch(Shade) the support of (X₁, X2). 21(ii.) Find the marginal density function of X₁. 21(iii.) Find the marginal density function of X₂. 21(iv.) Find E[X₁]. 21(v.) Find E[X₂]. 21(vi.) Find the conditional density of X₂ given X₁ = ₁, i.e., fx₂|X₁ (x2|x₁). 21(vii.) Find the conditional expectation of X₂ given X₁ = x₁, i.e. E[X₂|X₁ = x₁]. 21(viii.) What is E[X2|X₁]? Using the property of conditional expectation, verify that E[X₂] is the same as the one obtained in part 21 (v.). 21(ix.) Using the joint density directly, find E[X₂] and verify that it is the same as obtained Q1(v.) and Q1 (viii.). 21(x.) Using the joint density directly, find E[X₁ - X₂]. 21(xi.) Using the joint density directly, find E[X₁ X₂], and the Cov(X1, X₂).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
solve parts 7,8,9 please
Thank you
![Q1 Let (X₁, X₂) be jointly continuous with joint probability density function
"
f(x1, x₂) = x1
0<x₂ < x₁ <1,
otherwise.
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., ƒx₂|X₁ (x2|x1).
Q1(vii.) Find the conditional expectation of X₂ given X₁ = x₁, i.e. E[X2|X₁ = x1].
Q1(viii.) What is E[X₂|X₁]? 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2F0949f0ff-e80c-4e55-86b9-ce021638d4d8%2Fpnad9vd_processed.png&w=3840&q=75)
Transcribed Image Text:Q1 Let (X₁, X₂) be jointly continuous with joint probability density function
"
f(x1, x₂) = x1
0<x₂ < x₁ <1,
otherwise.
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., ƒx₂|X₁ (x2|x1).
Q1(vii.) Find the conditional expectation of X₂ given X₁ = x₁, i.e. E[X2|X₁ = x1].
Q1(viii.) What is E[X₂|X₁]? 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).
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