See the distribution change
Pick one, move a parameter, and watch what happens to the shape. The mean and variance follow along, and the numbers behind the picture are printed underneath.
The numbers behind the picture
| x | density or probability |
|---|
Why this is worth playing with
Most students learn a distribution as a formula and a pair of moments, and never see what the formula does. Move the shape parameter on a gamma from 1 to 10 and you can watch it turn from the exponential into something very nearly normal — which is the whole of why the central limit theorem turns up where it does.
Every curve here is drawn from the density itself, not from a picture someone traced. The mean marked on the chart is the closed form, and each one is checked against a numerical integral of its own density when the page loads: if a formula and its own curve ever disagreed, this page would say so rather than draw it.