I am doing a problem that reads
Suppose $X_1, X_2..., X_n$ are independent random variables with common expectation $\mu$ and variance $\sigma^2$. Let $S_n$=$X_1+X_2+...+X_n$. Find the expectation and variance of $S_n$ repeat for $S_n/n$.
I am kind of at a loss. I assumed the expectation would remain the same for $S_n$, if I have two random variables that can take on the same values and have the same expectation, wouldn't the expectation remain the same because I would be doubling both the numerator and the denominator?