# Math Help - correlation coefficient

1. ## correlation coefficient

The correlation coefficient between x and y is 0.85

Statement 1-then the correlation coefficient between x/2 and y/2 is 0.85/2
Statement 2-then the correlation coefficient between - X and Y is - 0.85

how are above two statements true?

2. ## Re: correlation coefficient

Use the definition of the correlation coefficient

$\frac{E[XY]-E[X]E[Y]}{\sigma(x) \sigma(y)}$ and these properties
$E[aX] = aE[X]$ and $Var(aX) = a^2Var(X)$.

Also i believe the first statement is not true. I get that $Cov(X/2,Y/2) = 1/4Cov(X,Y)$ and that
$\sigma_{X/2} = \sqrt{Var(X/2)} = \sqrt{1/4Var(X)} = 1/2\sigma_X$
You can find the variance of $Y/2$ the same way. Giving us that statement 1 is 0.85.