Concept

Binomial distribution

The distribution of how many successes come out of a fixed number of independent trials with the same chance each. Its mean is the number of trials times the chance of success, and its spread grows like the square root of that number.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A Galton board after 600 balls. 600 balls fall through 12 rows of pegs, each bouncing left or right at random, and pile up in a bell-shaped heap.

A bell curve assembled out of coin flips

Drop six hundred balls through a board of pegs, each bouncing left or right at random, and they pile up in a shape that can be predicted precisely. Nothing coordinated them.

probability · Central limit

Nine walks, and the square root. 9 independent walks of 400 steps, each step one place left or right. The dashed curves are ±√n: the walks stay near them, spill past them, and come back — which is what a typical distance means as opposed to a limit.

A walk that always comes home, until it does not

Step left or right at random, forever, and the walk returns to where it started with certainty. On a grid it also returns. In space it does not, and about a third of walks leave and never come back.

probability · Random walk

Named alongside it

The objects these essays reach for when they reach for this one.

Convergence Independence Limit Normal distribution Diffusion Galton board Heavy tails Parity Pi Random walk Recurrence Transience

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