Modern Probability Theory and its Applications.
Modern Probability Theory and its Applications.
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DOI：
10.1021/ja01472a052
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发表时间：
1961-06
影响因子：
15
通讯作者：
L. Sucheston
中科院分区：
文献类型：
--
作者：
L. Sucheston
现代概率论及其应用。作者：Emanuel Parzen，斯坦福大学统计学副教授。 John Wiley and Sons, Inc.，440 Fourth Avenue, New York 16, N.. 1960。xv+ 464 页。15.5 X 23.5 厘米。价格，10.75 美元。这本书的标题也许应该是：概率论导论，因为按照数学标准，它是第一本本科生教科书。内容：第一章，概率论作为随机现象数学模型的研究；第二章，基本概率论；第三章，独立与依附；第四章，数值随机现象；第五章，概率律的均值和方差；第六章，正态、泊松和相关概率定律；第七章，随机变量，第八章，随机变量的期望；第九章，独立随机变量之和；和第十章，随机变量序列。不假设勒贝格积分的知识。有些定理是在没有证明的情况下陈述的，作者通常会仔细地指出这一事实。本书文笔生动，包含有趣的书目和历史评论。值得一提的几点： 第一章-TI 中对组合学要素的详细处理；给定随机变量的事件的条件概率的定义，不使用 Radon-Nikodym 定理，第七章；一篇关于随机变量信噪比测量的文章，第八章；用特征函数的方法处理分布收敛性，包括第九章特征函数反演公式的证明，第十章“概率论连续性定理”的证明。一个小缺陷：函数的定义，p。 269，不正确。总之，将这部作品与该领域的经典论文 Feller 的《概率论及其应用导论》进行比较可能是合适的。以将自己限制在离散情况为代价，费勒实现了数学上令人钦佩且完全独立的处理。然而，审稿人认为帕森的书更适合作为本科生教科书：它更容易理解，并且也处理了连续的案例。
Modern Probability Theory and its Applications. By Emanuel Parzen, Associate Professor of Statistics, Stanford University. John Wiley and Sons, Inc., 440 Fourth Avenue, New York 16, N.. 1960. xv+ 464 pp. 15.5 X 23.5 cm. Price, $10.75. The title of this book should perhaps be: Introduction to Probability Theory, since by mathematical standards it is a first undergraduate textbook. Content: Chapter I, Proba-bility Theory as the Study of Mathematical Models of Random Phenomena; Chapter II, Basic Probability Theory; Chapter III, Independence and Dependence; Chapter IV, Numerical-Valued Random Phenomena; Chapter V, Mean and Variance of a Probability Law; Chapter VI, Normal, Poisson, and Related Probability Laws; Chapter VII, Random Variables, Chapter VIII, Expectation of a Random Variable; Chapter IX, Sums of Independent Random Variables; and Chapter X, Sequences of Random Variables. The knowledge of Lebesgue integration is not assumed. Some theorems are stated without proof, the author usually pointing out this fact carefully. The book Is written vividly, contains interesting bibliographical and historical remarks. Some points worth mentioning: Detailed treatment of ele-ments of combinatorics in Chapters I—TI; definition of con-ditional probability of an event given a random variable, without use of the Radon-Nikodym theorem, Chapter VII; an article on the measurement of the signal-to-noiseratio of a random variable, Chapter VIII; treatment of convergence in distribution by the method of characteristic functions, including in Chapter IX the proof of the inversion formulas for characteristic functions, in Chapter X the proof of the" continuity theorem of Probability Theory.” A trivial flaw: the definition of a function, p. 269, is not correct. In conclusion, it may be appropriate to compare this work with the classic treatise in the field, Feller’s" Introduction to Probability Theoryand Its Applications.” At the price of limiting himself to the discrete case Feller achieves a mathematically admirable and completely self-contained treatment. The reviewer feels, however, that Parzen’s book is to be preferred as an undergraduate textbook: it is considerably easier to understand and also treats the con-tinuous case.