Let $G$ be a random variable with $G=G(X,Y)$ where $G(x,y)=3x+y^2$. find $E(G)$

Question

Let $G$ be a random variable with $G=G(X,Y)$ where $G(x,y)=3x+y^2$. Find $E(G)$

i know that $E(X)=E(Y)=1$ and $Var(X)=Var(Y)=1/2$

is this enough to answer the question?

Im sure this is'nt too hard but i'm having a mind blank, could someone clear this up for me?

Answer 1

Linearity of expectation gives us here: $$\mathbb EG=3\mathbb EX+\mathbb EY^2$$

To find $\mathbb EY^2$ you can make use of: $$\text{Var}Y=\mathbb EY^2-(\mathbb EY)^2$$