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Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for {,}, from validity for some r we deduce validity for +.
The bounds these inequalities give on a finite sample are less tight than those the Chebyshev inequality gives for a distribution. To illustrate this let the sample size N = 100 and let k = 3. Chebyshev's inequality states that at most approximately 11.11% of the distribution will lie at least three standard deviations away from the mean.
In mathematics, the following inequality is known as Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful inequality of Nairi Sedrakyan published in 1997, [1] to the book Problem-solving strategies of Arthur Engel published in 1998 and to the book Mathematical Olympiad Treasures of Titu ...
A power inequality is an inequality containing terms of the form a b, where a and b are real positive numbers or variable expressions. They often appear in mathematical olympiads exercises. Examples: For any real x, +.
The rearrangement inequality can be regarded as intuitive in the following way. Imagine there is a heap of $10 bills, a heap of $20 bills and one more heap of $100 bills.
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