There are 2 random variables, X and Y. The $E(X) = -1\; and\;E(Y)=6$
I also know that $Var(X) = 6 \; and \; Var(Y) = 9 \; and \;Cor(X,Y)=0.9$
How can i calculate $Var(X+10Y)$ ?
I tried to calculate this by using this formula:
$Var(X±Y)=Var(X)+Var(Y)±2Cov(X,Y)$
With poor success.
Do i have to calculate new variance for 10Y and new Covariance with X and 10Y or how this should be done ?
Some hints would be most welcome.
Hint:
Use: $\mathsf {Var}(a\,Y) = a^2\,\mathsf {Var}(Y)$
Also: $\mathsf {Cov}(a\,X,b\,Y) = a\,b\,\mathsf {Cov}(X,Y)$
PS: remember that: $\mathsf{Cor}(X,Y) =\frac{\mathsf{Cov}(X,Y)}{\sqrt{\mathsf{Var}(X)\mathsf{Var}(Y)}}$