Need someone to quickly confirm whether I have this expected value correct

Question

I am given that $E(X)=2$, $E(Y)=4$, $E(X^2)=6$, $E(Y^2)=20$ and $E(XY)=1$.

I am asked to calculate $E((3X-2)^2)$ - would I be correct in representing this as $9E(X^2)-12E(X)+4$ so my answer would be $34$. Is that correct?

Answer 1

You are correct: the expectation value $E[\cdot]$ is a linear functional, i.e. $E[aX+bY]=aE[X]+bE[Y]$. Then $E[(3X-2)^2]=E[9X^2-12X+4]=9E[X^2]-12E[X]+4=34.$