Let $X$ and $Y$ be two discrete random variables such that $Y=X+a$. what is the mean of $Y$, $\mu_y$ with respect to $\mu_x$, the mean of $X$? Why does this make sense?
$Y=X+a$
$E(Y)=E(X+a)=E(X)+E(a)=E(x)+a$
I'm just a little confused on the "why does this make sense" part. Is the correct answer: this makes sense because of the linearity of expectation?
I agree that the phrasing of the question is a little odd, but I reckon that they're probably looking for an intuitive explanation such as "because $a$ shifts the probability distribution of $X$, and so we would expect the mean of $Y$ to be the shifted mean of $X$". Or something along those lines.