Markov's inequality states that the probability of a positive random variable exceeding a given value is less than or equal to the expected value of the random variable divided by the given value, and Kolmogorov's inequality limits the sum of random variables.
This statement can be proven using Markov's inequality, and it can be used to prove the weak law of large numbers and Kolmogorov's inequality. Markov's inequality states that the probability of a positive random variable exceeding a given value is less than or equal to the expected value of the random variable divided by the given value, and Kolmogorov's inequality limits the sum of random variables. One consequence of this theorem is that the difference between the mean and median of a set of numbers is less than the standard deviation. Name this statement that the probability that the distance from a number in a distribution to the expected value is greater than k standard deviations is always less than or equal to one over k squared.
This statement can be proven using Markov's inequality, and it can be used to prove the weak law of large numbers and Kolmogorov's inequality.
Chebyshev’s inequality [or Chebyshev’s theorem]