i have another qns here if the correlation coefficient between X and Y is ρxy=1 how to prove that σ(X+Y) = σX + σY ?
Follow Math Help Forum on Facebook and Google+
Hello, By definition, $\displaystyle 1=\rho_{XY}=\frac{cov(X,Y)}{\sigma_X\sigma_Y} \Rightarrow cov(X,Y)=\sigma_X\sigma_Y$ (1) But we know that $\displaystyle \sigma^2(X+Y)=\sigma^2_X+\sigma^2_Y+2 cov(X,Y)$ (2) Just replace (1) in (2) and you're done.
ok! i got it! thanks!! =D
View Tag Cloud