|
Markov Inequality
In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function (mathematics), function of a random variable is greater than or equal to some positive Constant (mathematics), constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in Mathematical analysis, analysis, refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Irénée-Jules Bienaymé, Bienaymé's inequality. Markov's inequality (and other similar inequalities) relate probabilities to expected value, expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Statement If is a nonnegative random variable and , then the probability that is at least is at most th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Inequality
In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function (mathematics), function of a random variable is greater than or equal to some positive Constant (mathematics), constant. It is named after the Russian mathematician Andrey Markov, although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in Mathematical analysis, analysis, refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second Chebyshev inequality) or Irénée-Jules Bienaymé, Bienaymé's inequality. Markov's inequality (and other similar inequalities) relate probabilities to expected value, expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Statement If is a nonnegative random variable and , then the probability that is at least is at most th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
