1. The problem statement, all variables and given/known data
Not exactly a homework question, but rather a section in Statistical Data Analysis:
Suppose there is a pdf y[SUB](x)[/SUB] that is not completely known, but μi and Vij are known:
2. Relevant equations
3. The attempt at a solution
I understand how <y(x) > ≈ y(μ),
My confusion:
Why does <y(x2) >
1. Imply we square everything throughout?
<[y(μ) + Ʃ[∂y/∂x](xi - μi)]2>
2. give a xi and xj term? Where did the xj come from?
3. Why is it for i≠j when xi and xj are uncorrelated, the expression simplifies to
σ2y ≈ Ʃ[∂y/∂x]2σ2i
Where did the j go?
Not exactly a homework question, but rather a section in Statistical Data Analysis:
Suppose there is a pdf y[SUB](x)[/SUB] that is not completely known, but μi and Vij are known:
2. Relevant equations
3. The attempt at a solution
I understand how <y(x) > ≈ y(μ),
My confusion:
Why does <y(x2) >
1. Imply we square everything throughout?
<[y(μ) + Ʃ[∂y/∂x](xi - μi)]2>
2. give a xi and xj term? Where did the xj come from?
3. Why is it for i≠j when xi and xj are uncorrelated, the expression simplifies to
σ2y ≈ Ʃ[∂y/∂x]2σ2i
Where did the j go?
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