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Biography. Ross received his B. S. degree in mathematics from Brooklyn College in 1963, his M.S. degrees in mathematics from Purdue University in 1964 and his Ph.D. degree in Statistics from Stanford University in 1968, studying under Gerald Lieberman and Cyrus Derman. He served as a Professor at the University of California, Berkeley from 1976 ...
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 ...
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 ...
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 ...
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 ...
Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example USS Scorpion, and has played a key role in the recovery of the flight recorders in the Air France Flight 447 disaster of 2009. It has also been used in the attempts to locate the ...
Conditional probability distribution. In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. Given two jointly distributed random variables and , the conditional probability distribution of given is the ...
M/G/1 queue. In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are M arkovian (modulated by a Poisson process ), service times have a G eneral distribution and there is a single server. [1] The model name is written in Kendall's notation, and is an extension of the M/M ...