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Titlebook: Probability Theory; Independence Interch Yuan Shih Chow,Henry Teicher Textbook 19781st edition Springer-Verlag New York Inc. 1978 Probabili

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發(fā)表于 2025-3-21 16:28:05 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Probability Theory
副標(biāo)題Independence Interch
編輯Yuan Shih Chow,Henry Teicher
視頻videohttp://file.papertrans.cn/757/756886/756886.mp4
圖書封面Titlebook: Probability Theory; Independence Interch Yuan Shih Chow,Henry Teicher Textbook 19781st edition Springer-Verlag New York Inc. 1978 Probabili
描述Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub- ject, generally attributed to investigations by the renowned french mathe- matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure- theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment whic
出版日期Textbook 19781st edition
關(guān)鍵詞Probability; Probability theory; Wahrscheinlichkeit; Wahrscheinlichkeitsrechnung; law of large numbers
版次1
doihttps://doi.org/10.1007/978-1-4684-0062-5
isbn_softcover978-1-4684-0064-9
isbn_ebook978-1-4684-0062-5
copyrightSpringer-Verlag New York Inc. 1978
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發(fā)表于 2025-3-21 20:56:07 | 只看該作者
Independence,dependent development. In the course of this evolution, probability theory has been fortified by its links with the real world, and indeed the definition of independence is the abstract counterpart of a highly intuitive and empirical notion. Independence of random variables {..}, the definition of w
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Distribution Functions and Characteristic Functions,rems of interest are geared to d.f.s of r.v.s and the majority of proofs are simpler and more intuitive when couched in terms of r.v.s having, or probability measures determined by, the given d.f.s. Since r.v.s possessing preassigned d.f.s can always be defined on some probability space, the languag
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Limit Theorems for Independent Random Variables,e available when the underlying random variables are merely independent and have recently been obtained for the strong law as well. Unfortunately, the practicality of the latter conditions leaves much to be desired.
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Infinitely Divisible Laws,.v.s, say {X.,. ≥ 1} have merely absolute moments of order ., then for . ≥ 2 only the normal distribution can arise as a limit, while if 0 < . ≤ 2, the limit law belongs to a class called stable distributions. If the basic r.v.s are merely independent (and infinitesimal when normed cf. (1) of Sectio
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