Probability Distributions
Shape the classic distributions by hand. Adjust the parameters of the normal, exponential, Poisson, and binomial distributions and watch mean and variance respond.
Probability DistributionsLive
PDF / PMF explorer
Controls
Presets
Data Inspector
Distributionnormal
Mean0.000
Variance1.000
Std dev1.000
Governing equation
Reading this result: The mean μ only slides the bell sideways while σ sets its width — variance is σ² = 1.00, so doubling σ quadruples the spread.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Each distribution's probability density (or mass) function is plotted live as you change its parameters, with the mean and variance computed exactly. It's the fastest way to build intuition for the distributions behind statistics, uncertainty quantification, and Monte-Carlo methods.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
More Math simulations
Frequently asked questions
Is this probability distribution tool really free?▾
Yes. Probability Distributions runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.