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Correlation Coefficient Assignment | Professional Writing Services

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December 9th, 2019

“(X_i,Y_i), i=1,2,..n is a sequence of independent identically distributed random variables. X_i and Y_j are independent when i ≠j. Define S_x = the sum from i= 1 to n of X_i S_y = the sum from i= 1 to n of Y_i Let (σ_x)^2 = Var(X_i), (σ_y)^2 = Var(Y_i),and ρ=Corr(X_i,Y_i), where Corr is the correlation coefficient.Find Corr(S_x , S_y)”

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Cov ( S _ X , S _ Y )V (S _ X ) ×V (S _ Y ) Corr(S_x , S_y) = ∑ ∑ Cov( X _ i,Y _ i) = i i ∑V ( X _ i, ∑V (Y _ i)i == = i ∑ ∑ (Corr ( X _ i, Y _ i) ×i V ( X _ i ) × V (Y _ i ) ) i…
 

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