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P(at least one estimation is bad) = 0.05 ≤ P(A 1 is bad) + P(A 2 is bad) + P(A 3 is bad) + P(A 4 is bad) + P(A 5 is bad) One way is to make each of them equal to 0.05/5 = 0.01, that is 1%. In other words, you have to guarantee each estimate good to 99%( for example, by constructing a 99% confidence interval) to make sure the total estimation ...
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 ...
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
The brief statement of Hölder's inequality uses some conventions. In the definition of Hölder conjugates, 1/∞ means zero. If p, q ∈ [1, ∞), then ‖ f ‖ p and ‖ g ‖ q stand for the (possibly infinite) expressions
In the context of metric measure spaces, the definition of a Poincaré inequality is slightly different.One definition is: a metric measure space supports a (q,p)-Poincare inequality for some , < if there are constants C and λ ≥ 1 so that for each ball B in the space, ‖ ‖ () ‖ ‖ ().
It can be generalized to any finite number n of points instead of 3, taken on the right-hand side k at a time instead of 2 at a time: [4] Let f be a continuous function from an interval I ⊆ R {\displaystyle I\subseteq \mathbb {R} } to R {\displaystyle \mathbb {R} } .
Christie has already played in two games with Dallas, versus the Sixers and Boston Celtics, scoring 15 points in each matchup and shooting 4-of-7 on 3-pointers, while averaging seven rebounds and ...
In mathematical analysis, the Minkowski inequality establishes that the L p spaces are normed vector spaces.Let be a measure space, let < and let and be elements of (). Then + is in (), and we have the triangle inequality