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7. A simple example of changing variables. a) Let x1, x2 be independent random variables. Let - u₁ = x1 - X2, = U2 x1 + x2. Assume we are given. V = ( στ x1 0 σ 02 x2 = 5, σx2 = 3, and evaluate V', Find V', the error matrix for u₁ and u₂. Substitute in σx₁ = 5, σx2 and hence σu₁ and Օ 2 • (b) Undoing the error propagation: u1 + u2 X1 = " 2 Աշ Ալ X2 = 2 What do you get for σ22, and σ22, (using the numerical values for σu₁ and биг found above) if you ignore correlations? x1 X2 Now use the correct matrix method to recover the expected V = ( 25 0 0 9

7. A simple example of changing variables. a) Let x1, x2 be independent random variables. Let - u₁ = x1 - X2, = U2 x1 + x2. Assume we are given. V = ( στ x1 0 σ 02 x2 = 5, σx2 = 3, and evaluate V', Find V', the error matrix for u₁ and u₂. Substitute in σx₁ = 5, σx2 and hence σu₁ and Օ 2 • (b) Undoing the error propagation: u1 + u2 X1 = " 2 Աշ Ալ X2 = 2 What do you get for σ22, and σ22, (using the numerical values for σu₁ and биг found above) if you ignore correlations? x1 X2 Now use the correct matrix method to recover the expected V = ( 25 0 0 9

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. A simple example of changing variables. a) Let x1, x2 be independent random variables. Let - u₁ = x1 - X2, = U2 x1 + x2. Assume we are given. V = ( στ x1 0 σ 02 x2 = 5, σx2 = 3, and evaluate V', Find V', the error matrix for u₁ and u₂. Substitute in σx₁ = 5, σx2 and hence σu₁ and Օ 2 • (b) Undoing the error propagation: u1 + u2 X1 = " 2 Աշ Ալ X2 = 2 What do you get for σ22, and σ22, (using the numerical values for σu₁ and биг found above) if you ignore correlations? x1 X2 Now use the correct matrix method to recover the expected V = ( 25 0 0 9
Transcribed Image Text:7. A simple example of changing variables. a) Let x1, x2 be independent random variables. Let - u₁ = x1 - X2, = U2 x1 + x2. Assume we are given. V = ( στ x1 0 σ 02 x2 = 5, σx2 = 3, and evaluate V', Find V', the error matrix for u₁ and u₂. Substitute in σx₁ = 5, σx2 and hence σu₁ and Օ 2 • (b) Undoing the error propagation: u1 + u2 X1 = " 2 Աշ Ալ X2 = 2 What do you get for σ22, and σ22, (using the numerical values for σu₁ and биг found above) if you ignore correlations? x1 X2 Now use the correct matrix method to recover the expected V = ( 25 0 0 9
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