Introduction to random variables

This document provides an introduction to random variables. It defines random variables as functions that assign real numbers to outcomes of an experiment. Random variables can be either discrete or continuous depending on whether their possible values are countable or uncountable. The document also defines probability mass functions (pmf) which describe the probabilities of discrete random variables taking on particular values. Expectation is introduced as a way to summarize random variables using a single number by taking a weighted average of all possible outcomes.