# Thread: standard deviation of 0.7X + 0.3Y?

1. ## standard deviation of 0.7X + 0.3Y?

X is normal with mean 9 and standard deviation 19
Y is normal with mean 11 and standard deviation 17
edit: the correlation between them is 0.6

What is the standard deviation of 0.7X + 0.3Y? I think I may know, but I want to be sure I'm getting it right.

2. ok , i'M not sure

0.7(19)+0.3(17) , i know it's simple

3. I don't think that is correct, based on rules for the standard deviation.

Could someone else help me with it please?

4. Originally Posted by paulrb
X is normal with mean 9 and standard deviation 19
Y is normal with mean 11 and standard deviation 17
edit: the correlation between them is 0.6

What is the standard deviation of 0.7X + 0.3Y? I think I may know, but I want to be sure I'm getting it right.
$\displaystyle Var(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)$

Standard Deviation=$\displaystyle \sqrt{variance}$

5. Thanks, I thought that's the formula I should use, but I wasn't sure of the relation between correlation and covariance?

is cov(X,Y) = (std. deviation X)(std. deviation X)(correlation) ?

6. correlation=COV(X,Y)/(STD Dev-x *STD Dev y)

I'm sorry, I misread correlation for covariance