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5. Suppose X = T (X₁, X2, X3) is a normal random vector with mean and covariance matrix X, where 2 1 30 1 0 1 Find the joint distribution of Y₁ = X₁ + X₂ + X3 and Y₂ = X₁ - X2. 1 1 μ = (2,1,2)T, Σ

5. Suppose X = T (X₁, X2, X3) is a normal random vector with mean and covariance matrix X, where 2 1 30 1 0 1 Find the joint distribution of Y₁ = X₁ + X₂ + X3 and Y₂ = X₁ - X2. 1 1 μ = (2,1,2)T, Σ

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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5. Suppose X = (X₁, X2, X3) is a normal random vector with mean and covariance matrix Σ, where 2 1 1 (H) 1 30 1 0 1 Find the joint distribution of Y₁ = X₁ + X2 + X3 and Y₂ = X₁ − X₂. 6. Suppose X is a two-dimensional normal random vector with joint density ƒ (11₁, #₂) = k^¹ exp{-}₂ (2² + 2x² − x122–3r₁ – 202 + 4) - 4)}. Find E(X) and Cov(X). μ = (2, 1, 2), Σ =
Transcribed Image Text:5. Suppose X = (X₁, X2, X3) is a normal random vector with mean and covariance matrix Σ, where 2 1 1 (H) 1 30 1 0 1 Find the joint distribution of Y₁ = X₁ + X2 + X3 and Y₂ = X₁ − X₂. 6. Suppose X is a two-dimensional normal random vector with joint density ƒ (11₁, #₂) = k^¹ exp{-}₂ (2² + 2x² − x122–3r₁ – 202 + 4) - 4)}. Find E(X) and Cov(X). μ = (2, 1, 2), Σ =
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