2.1 Random Variables

Random variables are foundational to understanding probability and statistics. When we typically think of variables, we consider them as being determinate, but in the context of probability, we are often dealing with uncertain or random outcomes. Hence, a "random variable" is a means of translating these uncertain outcomes into a definite numeric form. Despite its name, a random variable is actually a function. It doesn't vary in the way typical variables do. Instead, it assigns a specific number to every possible outcome of a random experiment.

Formally, it can be defined as:

Given a sample space  of a random experiment (the set of all possible outcomes), a random variable  is a function that maps every outcome  in  to a real number.

This definition implies that for every outcome  in the sample…