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Sheldon M. Ross is the Daniel J. Epstein Chair and Professor at the USC Viterbi School of Engineering. He is the author of several books in the field of probability. He is the author of several books in the field of probability.
Ross's conjecture. In queueing theory, a discipline within the mathematical theory of probability, Ross's conjecture gives a lower bound for the average waiting-time experienced by a customer when arrivals to the queue do not follow the simplest model for random arrivals. It was proposed by Sheldon M. Ross in 1978 and proved in 1981 by Tomasz ...
In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question. If the distribution of X is discrete and ...
Maximum-minimums identity. In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2 n − 1 non-empty subsets of S . Let S = { x1, x2, ..., xn }. The identity states that. or conversely. For a probabilistic proof, see the reference.
MIAR · NLM (alt) · Scopus. ISSN. 0269-9648 (print) 1469-8951 (web) Links. Journal homepage. Probability in the Engineering and Informational Sciences is a peer-reviewed scientific journal published by Cambridge University Press. The founding editor-in-chief is Sheldon M. Ross (University of Southern California). [1]
Ilan Adler and Sheldon M. Ross, "Distribution of the Time of the First k-Record", Probability in the Engineering and Informational Sciences, Volume 11, Issue 3, July 1997, pp. 273–278 Ron Engelen, Paul Tommassen and Wim Vervaat, "Ignatov's Theorem: A New and Short Proof", Journal of Applied Probability, Vol. 25, A Celebration of Applied ...
Chapman–Kolmogorov equation. In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation (CKE) is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. The equation was derived independently by both the ...
The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. [1] These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. [2] There are several other (equivalent) approaches to formalising ...