Titlebook: Probability via Expectation; Peter Whittle Textbook 2000Latest edition Springer Science+Business Media New York 2000 Markov process.Marti

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Continuous Random Variables and Their Transformations,hat there were at most countably many realizations. However, we were increasingly led to consider r.v.s . on more general sample spaces, and it became evident in Section 7.5 that we need to be able to calculate the distribution of functions of . in terms of the distribution of

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Markov Processes in Discrete Time,en natural to consider gaming (Section 4.5), renewal processes (Section 6.1) and population growth (Section 6.4) as situations evolving in time. Almost all real-world phenomena must be considered dynamically.

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978-1-4612-6795-9Springer Science+Business Media New York 2000

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Probability via Expectation978-1-4612-0509-8Series ISSN 1431-875X Series E-ISSN 2197-4136

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Some Basic Models,With the concepts of expectation and probability established, it is time to discuss a number of basic models. These are of interest both in themselves and because they indicate the way forward.

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Conditioning,The idea behind . is that a partial observation can give one some idea of where in sample space the ω specifying the realization must lie: in a set ., say. Then, in effect, the sample space has contracted: instead of taking expectations over the full space Ω, one does so only over

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Action Optimisation; Dynamic Programming,This and the following two chapters are something of a diversion, but open the way to important applications. The primal role of the expectation concept in all three cases is a fact of life rather than of selection.

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