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?
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?
Use the definition of the correlation coefficient
$\displaystyle \frac{E[XY]-E[X]E[Y]}{\sigma(x) \sigma(y)} $ and these properties
$\displaystyle E[aX] = aE[X] $ and $\displaystyle Var(aX) = a^2Var(X) $.
Also i believe the first statement is not true. I get that $\displaystyle Cov(X/2,Y/2) = 1/4Cov(X,Y)$ and that
$\displaystyle \sigma_{X/2} = \sqrt{Var(X/2)} = \sqrt{1/4Var(X)} = 1/2\sigma_X $
You can find the variance of $\displaystyle Y/2 $ the same way. Giving us that statement 1 is 0.85.