SOLUTION: A random variable X has mean 110 and standard deviation 18, and a random variable Y has mean 215 and standard deviation 30; and the correlation between X and Y is r=0.75. The stand

Question 503214: A random variable X has mean 110 and standard deviation 18, and a random variable Y has mean 215 and standard deviation 30; and the correlation between X and Y is r=0.75. The standard deviation of X+Y is [x]. (Round your answer to 2 decimal places.)
Answer by Sarpi(32) (Show Source): You can put this solution on YOUR website!
E(.)= the mean
s(.)= the standard deviation
So, E(X)=110 s(X)=18 ; E(Y)=215 s(Y)=30
r(X,Y)=0.75
The standard deviation of X+Y, formula;
"Var= "
The above formula comes from this general formula
note: a and b are equal to 1, the coefficient of X and Y
. We therefore need to find the covariance of X and Y
Formula: . The actual formula for finding the cov(x,y) is . We don't know the value of E(XY) so we use the alternative since r(x,y) is given.

Cov(x,y)=405
However,

That implies is equal to the standard deviation of X+Y
So, s(X+Y)=45.10
I hope you really understand the steps. And your feedback will be appreciated.
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