Search results
Results From The WOW.Com Content Network
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.
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.
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 probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck. The hypergeometric distribution, which describes the number of successes in the first m of a series of n consecutive Yes/No experiments, if the total number of successes is known. This distribution ...
where P(t) is the transition matrix of jump t, i.e., P(t) is the matrix such that entry (i,j) contains the probability of the chain moving from state i to state j in t steps. As a corollary, it follows that to calculate the transition matrix of jump t , it is sufficient to raise the transition matrix of jump one to the power of t , that is
Bertrand's box paradox: the three equally probable outcomes after the first gold coin draw. The probability of drawing another gold coin from the same box is 0 in (a), and 1 in (b) and (c). Thus, the overall probability of drawing a gold coin in the second draw is 0 / 3 + 1 / 3 + 1 / 3 = 2 / 3 .