Chebyshev's inequality
Desigualdad de Chebyshov
- Date
- 1867 · confidence high
- Place
- Saint Petersburg, Russia
- Credited to
- Pafnuty Chebyshev
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Chebyshev proved a general bound on the probability that a random variable departs from its mean by more than k standard deviations: at most 1/k², valid for any distribution with finite variance.
His friend and colleague Irénée-Jules Bienaymé had already proved a special case in 1853, hence it is sometimes called the Bienaymé-Chebyshev inequality. The Wikidata candidate gave no year; it is set here to 1867, that of Chebyshev's general proof.
What it led to
- Proof of the weak law of large numbers for variables with finite variance
- Concentration bounds used in modern statistics and probability theory
- Later generalisations (Bienaymé-Chebyshev, Cantelli inequalities)