Let x1 and x2 be jointly distributed random variables, Basic Statistics

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Let x1 and x2 be jointly distributed random variables

Let X₁ and X₂ be jointly distributed random variables possessing finite second moments. State conditions under which it is possible to find 2 uncorrelated random variables, Y₁ and Y₂ which are linear combinations of X₁ and X₂ (that is, Y₁= a₁₁X₁ + a₁₂X₂ and Y₂ = a₂₁X₁ + a₂₂X₂ for some constants an, a₁₂, a₂₁, a₂₂ and Cov [Y₁, Y₂] = 0).

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Basic Statistics: Let x1 and x2 be jointly distributed random variables

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Basic Statistics: Let x1 and x2 be jointly distributed random variables

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