Titlebook: Probability Models; John Haigh Textbook 2013Latest edition Springer-Verlag London 2013 Distributions.Markov Processes.Probability.Random V

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Conditional Probability and Independence,another . die were thrown, and their total score was four. Then you could be sure that the score on the blue die was not six. Similarly, to be told that the total score was ten makes it more likely that the blue die scored six, as all scores lower than four are eliminated. Information about the tota

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Sums of Random Variables,d notation in an analysis, are often a long stride towards the solution. In modelling random phenomena, we may find that . is either naturally the sum of other quantities ..,..,…,.., or can be conveniently written as such a sum. Especially when the components of this sum are independent, we can take

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Stochastic Processes in Discrete Time, Examples include the size of our capital after a series of investments in the stock market, or other casinos; the accumulated number of points of a football team during the season; a student’s Grade Point Average as she progresses through college; your own weight as you strive for the target you se

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Stochastic Processes in Continuous Time, exact probabilities and limiting values for a process having the Markov property, i.e. knowing the current state, we can ignore the path to that state. Similarly, in continuous time, it is a great mathematical convenience to assume this Markov property. We begin by looking at continuous time Markov

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John Haightion quantities follow near the percolation threshold, provides a clear description of the geometry of percolation clusters of the connected paths, and addresses several variations of percolation theory. In particular, bootstrap percolation, explosive percolation, and invasion percolation are featur

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John Haightion quantities follow near the percolation threshold, provides a clear description of the geometry of percolation clusters of the connected paths, and addresses several variations of percolation theory. In particular, bootstrap percolation, explosive percolation, and invasion percolation are featur