Probability: Expectation of a function.

Question

I've got a probability question where E(x)=5 , Var(x)=36 and Y = 0.7X + 2.

I need to determine the variance of Y using E(Y^2) and [E(Y)]^2.

I just can't figure out how to work out E(Y^2).

I can do it with the (a^2)*Var(x) formula but I'm not sure if I'm meant to use it or not.

Any help would be really appreciated.

Thanks

Answer 1

Hint:

What is $Y^2$? $$ Y^2=(0.7X+2)^2=0.49X^2+2.8X+4. $$ So, $$ \mathbb{E}[Y^2]=0.49\mathbb{E}[X^2]+2.8\mathbb{E}[X]+4. $$ Of course, to finish this, you need to know $\mathbb{E}[X^2]$; however, you can figure this out from knowing both $\mathbb{E}[X]$ and $\text{Var}[X]$.