What are probability distributions?

Probability distribution functions are functions that define the probability over possible values of random variables. They are intrinsically tied to random variables, as the two are mutually defined. Probability distribution functions are fundamental to machine learning, computer science, engineering, and the computational methods of all social and hard sciences.

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations. These formulations allow us to leverage computational power to perform predictions and inferences efficiently. Machine learning and data science are fundamentally fields of mathematical models. Any understanding of mathematical modeling begins with an understanding of calculus and probability. Familiarity with common probability distributions is at the center to that.

This article provides an introduction to random variables, and then moves into an overview of essential probability distributions that are central to modelling. It moves through a series of fundamental distributions, explaining their main applications and value.