Visualisation

A zoo of distributions

Last reviewed 4 May 2026

Bernoulli, Gaussian, exponential and beta side by side, each shaped by its own parameters.

From the chapter: Chapter 4: Probability

Glossary: bernoulli distribution, gaussian distribution, exponential distribution, beta distribution

Transcript

A handful of named distributions appear again and again in machine learning. Each is shaped by a small set of parameters that control its behaviour.

The Bernoulli distribution is the simplest. It assigns probability p to one outcome and one minus p to the other. Watch the bars rebalance as p slides from zero to one.

The Gaussian or normal distribution is the bell curve. It is governed by two numbers: a mean that shifts the peak, and a standard deviation that controls its width. Most of the probability mass sits within two standard deviations of the mean.

The exponential distribution describes the time between events in a memoryless process. A single rate parameter controls how quickly it decays.

The beta distribution lives on the unit interval and is the workhorse of probabilities of probabilities. Its two parameters can make it U-shaped, bell-shaped, skewed left, or skewed right.

These four shapes, with their handful of parameters, model a great amount of the world.

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