Q:

simple calculation question in statistic

i've been solving questions for hours as a preparation, and my mind doesn't work. i've done most of the steps needed to finish the calculation, but i always think i'm missing something in it.
the question:
having $Y=\frac{x-t}{2}$, where x is a random variable(normal) with mean t and variance 4. i need to calculate E[(x-t)^2].
what i did:
so i obtained that Y as given is standard normal with deviation 1 and mean 0. i calculated $E[Y^2]=1$ because of mean 0 and variance 1, and i am stuck here. 
please help me.
thank you very much for that

A:

You do not need any $Y$.

$E[(X-t)^2]$ is by definition the variance of $X$, as $t$ is the mean of $X$.
The variance of $X$ is also given to be $Var[X] = 4$.

So, 
$$E[(X-t)^2] = Var[X] = 4$$

