# standard deviation of 0.7X + 0.3Y?

• Oct 14th 2009, 05:05 PM
paulrb
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.
• Oct 14th 2009, 05:23 PM
donsmith
ok , i'M not sure

0.7(19)+0.3(17) , i know it's simple
• Oct 14th 2009, 05:31 PM
paulrb
I don't think that is correct, based on rules for the standard deviation.

Could someone else help me with it please?
• Oct 14th 2009, 05:45 PM
artvandalay11
Quote:

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.

$

Var(aX+bY)=a^2Var(X)+b^2Var(Y)+2abCov(X,Y)
$

Standard Deviation= $\sqrt{variance}$
• Oct 14th 2009, 05:52 PM
paulrb
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) ?
• Oct 14th 2009, 05:54 PM
artvandalay11
correlation=COV(X,Y)/(STD Dev-x *STD Dev y)

I'm sorry, I misread correlation for covariance