I'm taking an upper level Economics class and one of my assignments asks the question in the title.
I approached it by using one property of expectation: expectation of the sum is equal to expectation of it's parts.
So, I did:
$$E[(2X + 3)^2] = E[4X^2 + 12X + 9] = 4E[X^2] + 12 E[X] + E$$
I didn't get the right answer. I'm not even sure if what I did was the approach.
There's also second part to this question, which also asks for the variance VAR(2X + 5), given VAR(X) = 4. I can only think of one relevant property of the variance and it doesn't help with that question.
Anyone have an idea of how I should approach this?