Pafnuty Chebyshev: Difference between revisions

Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышев) (1821-1894) was a Russian mathematician. His name is also transliterated as Tchebysheff or Tschebyscheff.

The Chebyshev polynomials are named in his honor.

In analog electronic there exist a filter family named "Chebyshev filters".

He is also known for his work in the field of Probability and Statistics. Chebyshev's inequality say that the probability that a random variable is more than a standard deviations away from its mean is no more than 1/a². If μ is the mean (or expected value) and σ is the standard deviation, then we can state the relation as:

$P(\left|X-\mu \right|>a\sigma )\leq {\frac {1}{a^{2}}}$

for any positive real number a. Chebyshev's inequality is used to prove the weak law of large numbers.

See also:

• Chebotarev's density theorem - (algebraic number theory)