Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i) Suppose Y₁ = X₁ X₂. Find Var(Y₁). ii) Suppose Y₂ = X₁ − 2X2 – X3. Find Var(Y₂) and Cov(Y₁, Y₂).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) =
-2, Cov(X1, X3) = -1.
i) Suppose Y₁ = X1₁ X₂. Find Var(Y₁).
ii) Suppose Y₂ = X₁ − 2X2 — X3. Find Var(Y₂) and Cov(Y₁, Y₂).
Transcribed Image Text:= Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) = -2, Cov(X1, X3) = -1. i) Suppose Y₁ = X1₁ X₂. Find Var(Y₁). ii) Suppose Y₂ = X₁ − 2X2 — X3. Find Var(Y₂) and Cov(Y₁, Y₂).
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