## What are probability distributions?

Submitted by Marianne on January 7, 2022Probability distributions turn up in all areas of science (and in many *Plus* articles) so we've decided to have a closer look at them. The short explainers below explore what a probability distribution actually is, visit some of the most commonly used distributions, and a few important concepts in the probability context. So next time you're not sure what is going to happen next, don't despair: one of these distributions may well be able to help you deal with the uncertainty.

Maths in a Minute: Probability distributions — Here's a short and sweet introduction to probability distributions with a couple of easy examples.

Maths in a Minute: The binomial distribution — When you're repeating the same process over and over and want to know the chance you get a given sequence of outcomes, then binomial is the way to go.

Maths in a Minute: The Poisson distribution — If you know that an event happens three times an hour *on average*, then this doesn't mean it happens exactly three times every hour. So how many times is it going to happen in the next hour? That's the kind of situation where the Poisson distribution can help.

Maths in a Minute: The exponential distribution — If you know that an event happens three times an hour *on average*, then this doesn't mean it happens exactly every twenty minutes. So how long will you have to wait for it to happen? Here's where the exponential distribution comes in.

Maths in a Minute: The gamma distribution — This is related to the exponential distribution, only rather than asking "how long do I have to wait for one event to happen" you ask "how long do I have to wait until the event has happened two, three, four, or any other number of times?"

Maths in a Minute: The normal distribution — This is a heavy weight among probability distributions because it turns up in many, many different situations. Here's a quick introduction.

Maths in a Minute: The central limit theorem — The central limit theorem is a reason why the normal distribution is so ubiquitous, so we've included it here.

Maths in a Minute: Expectation — The expectation, also called the mean, of a probability distribution gives you a sense of what you'll see on average. This article explains how.

Maths in a Minute: Variance — The variance of a probability distribution gives you a sense of how spread out the probabilities captured by a distribution are. This article explains how.