In my Stats course (can't ask prof, it's an online course), we got to random variables and the notation has changed from using $s^2$, $\bar{x}$, etc...to using what we were initially taught are the symbols used to describe population as opposed to sample; namely $\sigma$, $\mu$, etc...
Why are we using population symbols when talking about random variables? Do we not use random variables for prediction or inference? And if we do, then aren't those samples?
I thought I understood that population is the entire data set we're interested in and that inference is done using a sample of that population, because if we already had the entire data set we're interested in there's no inference to be done since we have all the information we need.
It seems to me that if we want to talk about the probability of something happening, we're interested in the behavior of elements we don't currently have in our data set; that should imply that what we currently have is not the population, but a sample.
In this case, why not use population symbols and for example $\frac{1}{n-1}$ instead of $\frac{1}{n}$?
EDIT: For example, when talking about the variance of a random variable, the formula given to us is: $$\sigma^2 = Var(X) = E[X^2] - (\mu_x)^2 $$