A. M. 莫拉和 P. N. 拉蒂的《概率与统计》

English | PDF | 1977 | 420 Pages | ISBN : 1349027693 | 26.1 MB

This book is an introduction to basic statistical concepts and their applications. The only prerequisite is some knowledge of differential and integral calculus, which can be picked up in fifteen one-hour lectures. All other mathematical requirements are given in the book itself, in the form of technical notes. The book is intended to give a clear picture of basic statistical concepts. Since the theory of sets is usually taught in secondary schools, only the concepts needed for a meaningful discussion of basic probability theory and statistical populations are discussed; the utmost care is taken to make the treatment rigorous at the mathematical level assumed. Every concept is properly defined and illustrated with examples and counter examples. The important points are specifically made in ' comments ' following the examples. A sufficient number of problem for a complete understanding of the topics discussed is given at the end of each section, and an additional set of problems appears at the end of each chapter, some of which supplement the theory in that chapter. Answers to these problems are provided at the end of the book. Also a number of statistical decision problems are included following the discussion of mathematical expectation. Acceptance sampling and quality control problems are discussed after introducing probability models, with a view to giving some practical applications of the models. A brief introduction to the topic of entropy is also given. Other applications have been omitted to keep the book to a manageable size. All the important results, correspondences and relationships are given in tabular form for quick reference. Most of the illustrations are taken from daily life, keeping in mind the age group of students for whom the book is intended. It is suggested that the book be used for a twenty-five-week course of three hours per week, given as a first course in statistics for arts, science, commerce and engineering students. This could usefully be supplemented by an additional one-hour problems session each week for those students who have difficulty with the subject.

这本书介绍基本的统计概念及其应用。唯一的要求是掌握一些微积分和积分的知识，可以在十五个一小时的课程中完成学习。书中的所有数学要求都以技术笔记的形式给出。本书旨在提供一个清晰的基本统计概念的画面。由于集合论通常在中学教育中教授，书中只讨论了基本概率论和统计总体有意义讨论所需的观念；尽最大努力确保在假设的数学水平上进行处理严格。每一个概念都被正确定义，并通过例子和反例进行说明。重要的观点会以每段中的“注释”来强调。每个部分末尾给出了足够的习题，以便理解讨论的主题。每一章末还附有额外的一套问题，其中有些补充了该章节的理论内容。这些问题的答案在书末给出。此外，在讨论数学期望之后还包含了一些统计决策问题。在接受抽样和质量控制问题中讨论概率模型时，目的是给这些模型提供一些实际的应用例子。书中也简要介绍了熵的概念。其他应用被省略是为了保持书籍在一个可管理的大小。所有的重要结果、对应关系和相互关系都被表格的形式给出以快速参考。大多数插图都是来自日常生活，在考虑到这本书的目标读者的年龄组的同时选取的。建议用每周三个小时，共二十五周的时间来使用这本书作为艺术、科学、商业和工程学生的基础统计学课程的第一门课。对于一些难以理解该主题的学生，可以每周额外安排一小时的问题讨论会来补充这本教材。

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