Let X 1 ,X 2 , and X 3 be three random variables with means, variances, and correlation coefficients, denoted by 1 , 2 , 3 2 1, 2 2 , 2 3 and 12 , 13 , 23 , respectively For constants b 2 and b 3 , suppose E(X 1 1 x 2 , x 3 ) b 2 (x 2 2 ) b 3 (x 3 3 ) Determine b 2 and b 3 in terms of the variances and the correlation coefficients

Question: Let X 1 ,X 2 , and X 3 be three random variables with means, variances, and correlation coefficients, denoted by 1 ,

Let X₁,X₂, and X₃ be three random variables with means, variances, and correlation coefficients, denoted by μ₁, μ₂, μ₃; σ²_1, σ²₂, σ²₃; and ρ₁₂, ρ₁₃, ρ₂₃, respectively. For constants b₂ and b₃, suppose E(X₁−μ₁|x₂, x₃) = b₂(x₂−μ₂)+b₃(x₃−μ₃). Determine b₂ and b₃ in terms of the variances and the correlation coefficients.

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Expanding EX11x2 x3 and rearranging the terms we have EX11x2 x3 b2 b2b2 x22 ... View full answer

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