Probability Fact

Putting probability to work johndcook.com/blog/applied-p…

The expected number of cycles in a random permutation of n items is the nth harmonic number, asymptotically log n.

The intuition behind martingales and solving problems with them codeforces.com/blog/entry/110…

The science of waiting in line johndcook.com/blog/2019/01/2…

It is the so-called 'normal' distribution that is abnormal in the sense that it has many unique properties not possessed by any other. -- E. T. Jaynes

When is correlation transitive? terrytao.wordpress.com/2014/06/05/whe…

Identifying people from supposedly anonymous data johndcook.com/blog/2018/12/0…

I’d say “clumpy” rather than “biased”. x.com/kagakutetsugak…

Cornish-Fisher expansion en.wikipedia.org/wiki/Cornish%E…

The maximum of a finite set of iid Gumbel random variables has a Gumbel distribution.

Let V(n) be the number of distinct points visited by a random walk on Z². V(n) approaches πn/log n asymptotically.

Weighting an average to minimize variance johndcook.com/blog/2025/11/1…

What is the probability that a random binary matrix is invertible? johndcook.com/blog/2026/05/1…

“When you have eliminated the impossible, whatever remains is often more improbable than your having made a mistake in one of your impossibility proofs.” -- Steven Kass

Bertrand's ballot theorem en.wikipedia.org/wiki/Bertrand%…

A random variable is a measurable function on a probability space.

Computing normal probabilities with a simple calculator johndcook.com/blog/2021/03/1…

“If the numbers are not random, they are at least higgledy-piggledy.” — RNG researcher George Marsaglia

A probability space is a measure space such that the measure of the whole space is 1.

'Probabilistic' comes from Latin. 'Stochastic' comes from Greek.

Explaining probability to a jury johndcook.com/blog/explainin…