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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.
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 Rolski. [1]
The naming is sometimes attributed to Sheldon Ross' textbook Introduction to Probability Models, although he removed the reference in later editions. [2] Many statistics textbooks do present the result as the definition of expected value. [3]
A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.
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 ...
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 ).
Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
Some writers on probability call this the "conditional covariance formula" [2] or use other names. Note: The conditional expected values E( X | Z) and E( Y | Z) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z.