Q1 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂ and the marginal density of X₂. and fx₁, x₂(x1|x₂) = C1x1 x² 2 0
Q1 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂ and the marginal density of X₂. and fx₁, x₂(x1|x₂) = C1x1 x² 2 0
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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Could you solve the first 3 questions?
for 1st part please draw the graph (I want to see how to do it )
Thank you
![Q1 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂
and the marginal density of X2.
and
fx₁|x₂(x1|x₂)
=
C1x1
2
0< x₁ <£₂, 0 < x₂ <1
otherwise.
fx.(2₂) = { 0₂² 0<x₂ <1,
otherwise.
where C₁ and C₂ are constants.
Q1(i.) Sketch(Shade) the support of (X₁, X₂) and find the constants ₁ and ₂
Q1(ii.) Find the joint probability density function of (X₁, X₂).
Q1(iii.) Find the marginal density function of X₁.
Q1(iv.) Find E[X₁].
Q1(v.) Find E[X₂].
Q1(vi.) Find the conditional density of X₂ given X₁ = ₁, i.e., fx₂x₁ (₂|x₁).
Q1(vii.) Find the conditional expectation of X₁ given X₂ = x2, i.e. E[X₁|X₂ = x₂].
Q1(viii.) What is E[X₁|X₂]? Using the property of conditional expectation, verify that E[X₁] is the same as the one obtained in part
Q1 (iv.).
Q1(ix.) Using the joint density directly, find EX₁] and verify that it is the same as obtained Q1(iv.) and Q1(viii.).
Q1(x.) Using the joint density directly, find EX₁ - X2₂].
Q1(xi.) Using the joint density directly, find EX₁ X₂], and the Cov(X₁, X₂).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Fe79e282e-6d56-4b85-ae3c-c8711e264a7b%2Fflts337p_processed.png&w=3840&q=75)
Transcribed Image Text:Q1 Let (X₁, X₂) be jointly continuous random vector with the following information: you are given the conditional density of X₁ given X₂
and the marginal density of X2.
and
fx₁|x₂(x1|x₂)
=
C1x1
2
0< x₁ <£₂, 0 < x₂ <1
otherwise.
fx.(2₂) = { 0₂² 0<x₂ <1,
otherwise.
where C₁ and C₂ are constants.
Q1(i.) Sketch(Shade) the support of (X₁, X₂) and find the constants ₁ and ₂
Q1(ii.) Find the joint probability density function of (X₁, X₂).
Q1(iii.) Find the marginal density function of X₁.
Q1(iv.) Find E[X₁].
Q1(v.) Find E[X₂].
Q1(vi.) Find the conditional density of X₂ given X₁ = ₁, i.e., fx₂x₁ (₂|x₁).
Q1(vii.) Find the conditional expectation of X₁ given X₂ = x2, i.e. E[X₁|X₂ = x₂].
Q1(viii.) What is E[X₁|X₂]? Using the property of conditional expectation, verify that E[X₁] is the same as the one obtained in part
Q1 (iv.).
Q1(ix.) Using the joint density directly, find EX₁] and verify that it is the same as obtained Q1(iv.) and Q1(viii.).
Q1(x.) Using the joint density directly, find EX₁ - X2₂].
Q1(xi.) Using the joint density directly, find EX₁ X₂], and the Cov(X₁, X₂).
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