Statistics — Introduction to Random Variables + 5 more topics

In statistics, we often deal with experiments whose outcomes aren't certain. For example, if you flip a coin, you don't know if it'll be heads or tails until it lands. A random variable is simply a function that assigns a numerical value to each possible outcome of a random experiment. This lets us use mathematical tools to analyze these outcomes.

We usually denote random variables with capital letters like $X$, $Y$, or $Z$. The actual value they take on for a specific experiment is written with lowercase letters, like $x$, $y$, or $z$.

A random variable is just a variable whose value is determined by the outcome of a random phenomenon. For instance, the number you get when rolling a die is a random variable. A Probability Distribution Function (PDF), or sometimes just a Probability Distribution, describes how the probabilities are distributed over the possible values of a random variable.

There are two main types of PDFs, depending on whether your random variable is discrete or continuous: