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

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https://doi.org/10.1007/978-1-4612-0509-8Markov process; Martingale; Probability Theory; Random variable; optimization; probability measure

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Uncertainty, Intuition, and Expectation, uncertainty, expect, believe. Nevertheless, as with many concepts for which we have a strong but rather vague intuition, the idea of probability has taken some time to formalize. It was in the study of games of chance (such as card games and the tossing of dice) that the early attempts at formaliza

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Applications of the Independence Concept,an appeal made explicit already in Section 4.1. Now that the concept has been set in the wider context of conditioning we can continue with the description of some further models which, while still standard, are of a more advanced character. These models are all somewhat individual. In Chapter 7 we

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The Two Basic Limit Theorems,behaviour of the sums. and averages . of such variables as . becomes large. The motivation is clear from the discussion of Section 1.2. Sample averages of actual data are observed to ‘converge’ with increasing sample size, and it was this ‘limit’ which we idealized to provide the concept of an expec

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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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