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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
The test is untimed. Students are not permitted to bring calculators to the testing area, however a calculator will appear on screen for math questions. Whether taking the PERT in high school or for college placement, students are only permitted two opportunities to take the test. Preparing for the test, understanding the type of questions, and ...
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.
The feasible regions of linear programming are defined by a set of inequalities.. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1]
In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a 1, a 2, ..., a n are non-negative real numbers and let denote the kth elementary symmetric polynomial in a 1, a 2, ..., a n. Then the elementary symmetric means, given by = (),
In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away.
Such inequalities are of importance in several fields, including communication complexity (e.g., in proofs of the gap Hamming problem [13]) and graph theory. [14] An interesting anti-concentration inequality for weighted sums of independent Rademacher random variables can be obtained using the Paley–Zygmund and the Khintchine inequalities. [15]
There is no corresponding upper bound as any of the 3 fractions in the inequality can be made arbitrarily large. It is the three-variable case of the rather more difficult Shapiro inequality, and was published at least 50 years earlier.