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Monte Carlo: to find out the mean of $A$, find a variable $B$, $corr(A,B)=c$, and simulate $A + B(E(B)-B)$ instead of A. What is $B$? The choices of B are cov(a,b)/var(a), cov(a,b)/var(b), 1, -1

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$$corr(A,B)=\frac{E(A-E(A))E(B-E(B))}{\sigma_A\sigma_B}=c$$ $${E(B-E(B))}=\frac{c(\sigma_A\sigma_B)}{E(A-E(A))}$$ $$A+B({E(B)-B)}=A+\bigg(\frac{c(\sigma_A\sigma_B)}{E(A-E(A))}-B\bigg)B$$

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  • $\begingroup$ Thanks for your answer. But what is B? $\endgroup$
    – Mike Shore
    Jan 11, 2017 at 18:01
  • $\begingroup$ You must add more information so that I can help $\endgroup$
    – Nebo Alex
    Jan 12, 2017 at 3:00
  • $\begingroup$ The choices of B are cov(a,b)/var(a), cov(a,b)/var(b), 1, -1 $\endgroup$
    – Mike Shore
    Jan 13, 2017 at 2:59

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