# Math Help - Correlation coefficient

1. ## Correlation coefficient

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 ?

2. Hello,

By definition, $1=\rho_{XY}=\frac{cov(X,Y)}{\sigma_X\sigma_Y} \Rightarrow cov(X,Y)=\sigma_X\sigma_Y$ (1)

But we know that $\sigma^2(X+Y)=\sigma^2_X+\sigma^2_Y+2 cov(X,Y)$ (2)

Just replace (1) in (2) and you're done.

3. ok! i got it! thanks!! =D