Titlebook: Probability Through Problems; Marek Capiński,Tomasz Zastawniak Book 2001 Springer Science+Business Media New York 2001 Conditional probabi

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Limit Theorems,esults constitute an important part of probability theory because of their theoretical significance and practical consequences. Some proofs tend to be quite difficult, however, and are deferred to a more advanced course in probability. Instead, the consequences and applications will be highlighted here.

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Probability Through Problems978-0-387-21659-1Series ISSN 0941-3502 Series E-ISSN 2197-8506

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Modeling Random Experiments, or a journey by train (outcome: the delay of arrival at the destination measured in minutes). We may be vitally interested in answers to questions such as:.The mathematical investigation of such questions begins after we find a suitable mathematical model of the random situation. Only then can the

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Classical Probability Spaces,ly, so the probability of an event consisting of . outcomes is simply ./.. In the framework of general probability spaces, this means that we assume that Ω is a finite set (with m elements), Σ = 2., and .({.}) =1/. for each . ∈ Ω; hence, .. We shall call such probability spaces . and refer to . as t

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Fields,of a probability measure ., which means that if . is an event, then it makes sense to compute .(.). It is natural to ask questions like this: What is the probability of the union of two events (one or the other happens)? What is the probability of the intersection of two events (both happen)? What i

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Finitely Additive Probability,ikely is it that a given event . takes place?” The basic idea encapsulated in condition (b) of Definition 4.1 is that to measure a set, we can decompose it into finitely many disjoint pieces, measure each piece separately, and then add up the results. In Chapter 6, this will be extended by allowing

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Random Variables and Their Distributions,d adding the numbers shown. You win 9 dollars in case 2, 3, 11, or 12 comes out, or lose 10 dollars if the outcome is 7. Otherwise, you do not win or lose anything. This defines a function on the set of all possible outcomes {2, ... , 12}, the value of the function being the corresponding gain (or l