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# Pafnuty Chebyshev

Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (May 4 1821 - November 26 1894) was a Russian mathematician. His name is also transliterated as Chebyshov, Tchebycheff or Tschebyscheff (obsolete German transcription).

He was a student of Nikolai Brashman. His own most illustrious student was Andrei Markov.

He is known for his work in the field of probability and statistics. Chebyshev's inequality says that the probability that the outcome of a random variable is no less than a standard deviations away from its mean is no more than 1/a2:

$P(|X - {\mathbf E}(X)| \ge a\,\operatorname{sdev}(X)) \le \frac {1}{a^2}$

Chebyshev's inequality is used to prove the weak law of large numbers and the Bertrand-Chebyshev theorem (1845|1850).