Chebyshev's inequality
inequality applying to random variables with finite expected values
Facts
8 properties- Instance of
- concentration inequality, theorem[3]
- Defining formula
- \Pr(|X-\operatorname{E}[X]| \geq a) \leq \frac{\operatorname{Var}[X]}{a^3}
- Different from
- Chebyshev-Bienayme inequality[7]
- Discoverer or inventor
- Pafnuty Chebyshev[2]
- Maintained by WikiProject
- WikiProject Mathematics[9]
- Named after
- Pafnuty Chebyshev, Irénée-Jules Bienaymé[4][5]
- Said to be the same as
- Chebyshev-Bienayme inequality[6]
- Studied by
- probability theory[8]
🏷️ Also known as
en Bienaymé–Chebyshev inequality
en Chebyshev's inequality
ar متباينة تشيبيشيف
cs Čebyševova nerovnost
da Tjebysjovs ulighed
de Tschebyscheff-Ungleichung
el Ανισότητα Τσεμπισιόφ
el ανισότητα Τσέμπισεφφ
el ανισότητα Chebyshev
es desigualdad de Chebyshov
fa نابرابری چبیشف
fi Tšebyšovin epäyhtälö
fr inégalité de Bienaymé-Tchebychev
he אי-שוויון צ'בישב
hi चिबिश्योफ़ की असमानता
hu Csebisev-egyenlőtlenség
it disuguaglianza di Čebyšëv
ja チェビシェフの不等式
ko 체비쇼프 부등식
pl Nierówność Czebyszewa
🔖 Identifiers · 12
- OpenAlex ID
- C71564387
- Brockhaus Enzyklopädie online ID
- tschebyschew-ungleichung-arithmetik
- Encyclopædia Britannica Online ID
- topic/Chebyshevs-inequality
- Freebase ID
- /m/014jzr
- Great Russian Encyclopedia Online ID (2017)
- 4681045
- Great Russian Encyclopedia portal ID
- neravenstvo-chebyshiova-b1f0d6
- Lex ID
- Tjebysjovs_ulighed
- MathWorld ID
- ChebyshevInequality
- Microsoft Academic ID (discontinued)
- 71564387
- National Library of Latvia ID
- 000327250
- ScienceDirect topic ID
- mathematics/chebyshev-inequality, engineering/chebyshev-inequality
- Treccani's Enciclopedia della Matematica ID
- disuguaglianza-di-bienayme-cebysev
🔗 Connections
Instance of 2
Named after 2
Created notable works 1
Discoverer or inventor 1
Maintained by WikiProject 1
Studied by 1
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Summary
Chebyshev's inequality is a concentration inequality[1].
Body
Origins
Things named after include Pafnuty Chebyshev[4], a mathematician[10], 1821–1894[11], of Russian Empire[12], awarded the Order of Saint Anna, 1st class[13], specialised in probability theory[14] and Irénée-Jules Bienaymé[5], a statistician[15], 1796–1878[16], of France[17], awarded the Officer of the Legion of Honour[18], specialised in statistics[19].