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Let X₁, X2, X3 be independent & identically distributed standard normal random variables and let Y₁ ~ N(1,4) and Y₂ ~ N(0.9) where Y, and Y₂ are independent & also independent of the Xis, i=1,2,3. a) Give the joint pdf of X₁, X₂, X3 b.) What is the variance of ×? c.) Compute the covariance between X₁ X₂ +3X3 and 2Y₁ + Y3 d). Compute the X₁ X₂ + 3X3 correlation coefficient between and 2Y₁ + Y3.

Let X₁, X2, X3 be independent & identically distributed standard normal random variables and let Y₁ ~ N(1,4) and Y₂ ~ N(0.9) where Y, and Y₂ are independent & also independent of the Xis, i=1,2,3. a) Give the joint pdf of X₁, X₂, X3 b.) What is the variance of ×? c.) Compute the covariance between X₁ X₂ +3X3 and 2Y₁ + Y3 d). Compute the X₁ X₂ + 3X3 correlation coefficient between and 2Y₁ + Y3.

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
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Let X₁, X2, X3 be independent & identically distributed standard normal random variables and let Y₁ ~ N(1,4) and Y₂ ~ N(0.9) where Y, and Y₂ are independent & also independent of the Xis, i = 1,2,3. 9.) Give the joint pdf of X₁, X2, X3 b.) What is the variance of ×? c.) Compute the covariance between X₁ X₂ +3X3 and 2Y₁ + Y3 - d). Compute the X₁ - 12/2X₂ + 3X3 correlation coefficient between and 2Y₁+ Y3.
Transcribed Image Text:Let X₁, X2, X3 be independent & identically distributed standard normal random variables and let Y₁ ~ N(1,4) and Y₂ ~ N(0.9) where Y, and Y₂ are independent & also independent of the Xis, i = 1,2,3. 9.) Give the joint pdf of X₁, X2, X3 b.) What is the variance of ×? c.) Compute the covariance between X₁ X₂ +3X3 and 2Y₁ + Y3 - d). Compute the X₁ - 12/2X₂ + 3X3 correlation coefficient between and 2Y₁+ Y3.
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