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[1] [2] The term Chebyshev's inequality may also refer to Markov's inequality, especially in the context of analysis. They are closely related, and some authors refer to Markov's inequality as "Chebyshev's First Inequality," and the similar one referred to on this page as "Chebyshev's Second Inequality."
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
In mathematics, Chebyshev's sum inequality, named after Pafnuty Chebyshev, states that if ...
Chebyshev's sum inequality, about sums and products of decreasing sequences Chebyshev's equioscillation theorem , on the approximation of continuous functions with polynomials The statement that if the function π ( x ) ln x / x {\textstyle \pi (x)\ln x/x} has a limit at infinity, then the limit is 1 (where π is the prime-counting function).
In probability theory, the multidimensional Chebyshev's inequality [1] is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.
Chebyshev's inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. It was first formulated by his friend and colleague Irénée-Jules Bienaymé in 1853 and proved by Chebyshev in 1867.
When the Pembroke Pines Police Department called the staffer to follow up, he replied: “This ain’t no big deal,” while refusing to answer questions, according to the report. At YSI’s Broward Girls Academy, a 30-bed program less than a mile away from Thompson, 18-year-old Destinee Bowers didn’t want to go to an evening church service ...
the most common choice for function h being either the absolute value (in which case it is known as Markov inequality), or the quadratic function (respectively Chebyshev's inequality). Another useful result is the continuous mapping theorem : if T n is consistent for θ and g (·) is a real-valued function continuous at point θ , then g ( T n ...