For a random variable X, suppose that $E[X]=4$ and $Var(X)=9$. Then
(a.) $E[(3+X)^2]= ?$
(b.) $Var(2+4X)= ?$
I know the answer for (b.) is $4^2Var(X)=16*9=144$
But I do not know how to do (a.) especially with the square throwing me off. I know that if it was only $E(3+x)$, I would just use the formula for it to be $3+E(X)$. But because there is a square, I do not know how to solve it.
Using the equation $$\sigma^2 = E[X^2]- \left( E[X] \right)^2,$$ we get $E[X^2]=25.$ For part (a), we expand to get $$E[(3+X)^2]=E[9]+6E[X]+E[X^2]=58.$$