I am trying to understand the relationship of a Random Variable to a population and random samples. I understand that a Random Variable is a function that maps each event in a sample space to a number. In this context, what would be a sample space and mapping? Would each sample be governed by the probability mass function?

Do we think of each sample as a Random Variable that takes on values from a population (sample space) randomly? 

Or do we think of a population as a Random Variable and our sample as a random collection of those points?

I would appreciate if you can explain this to someone who is new to mathematical statistics. Thank you!