Take n random samples from the left distribution. Compute their average.
Plot it on the right. Repeat. No matter what the source looks like, the averages
form a bell curve. This is the central limit theorem — one of the most
surprising results in mathematics.
Source Distribution
Distribution of Means (n=5)
click & drag on the source panel to draw your own distribution
5
1/frame
samples: 0
mean: —
std: —
The Cauchy distribution has no finite mean or variance. The central limit theorem
requires finite variance to work. Watch what happens when that condition is violated —
the averages never settle into a bell curve, no matter how many samples you take.