概率論與數(shù)理統(tǒng)計(jì)

內(nèi)容概要

本書從Pearson出版公司引進(jìn)，由北京大學(xué)房祥忠等改編。本書包括概率論入門，經(jīng)典統(tǒng)計(jì)和現(xiàn)代統(tǒng)計(jì)的基礎(chǔ)部分，具體內(nèi)容包括：概率論，條件概率，隨機(jī)變量及其分布，數(shù)學(xué)期望，幾種特殊分布，估計(jì)，樣本分布和評(píng)估，假設(shè)檢驗(yàn)，范疇數(shù)據(jù)和非參數(shù)方法，線性統(tǒng)計(jì)模型，模擬。本書難度適中，只需初等微積分知識(shí)就可通覽，其概率部分是為統(tǒng)計(jì)服務(wù)的。本書統(tǒng)計(jì)部分比國(guó)內(nèi)教材豐富，引進(jìn)了一些現(xiàn)代統(tǒng)計(jì)處理技術(shù)。模型比較多，案例涉及面廣，實(shí)用性強(qiáng)，統(tǒng)計(jì)思想闡述與算法更為具體。本書是為高等院校理工科大學(xué)生學(xué)習(xí)概率統(tǒng)計(jì)課程編寫的教科書，科技人員也可從中獲益。

書籍目錄

序言 1 概率論引論   1.1 概率論歷史   1.2 概率的解釋   1.3 試驗(yàn)、事件和樣本空間   1.4 概率的定義   1.5 有限樣本空間   1.6 組合法   1.7 事件并的概率   1.8 補(bǔ)充練習(xí) 2 條件概率   2.1 條件概率的定義   2.2 獨(dú)立事件   2.3 貝葉斯定理   2.4 補(bǔ)充練習(xí) 3 隨機(jī)變量及其分布   3.1 隨機(jī)變量和離散分布   3.2 連續(xù)分布   3.3 分布函數(shù)   3.4 二元隨機(jī)變量的分布   3.5 邊緣分布   3.6 條件分布   3.7 多元隨機(jī)變量的分布   3.8 隨機(jī)變量的函數(shù)   3.9 兩個(gè)或多個(gè)隨機(jī)變基的函數(shù)   3.10 補(bǔ)充練習(xí) 4 期望   4.1 隨機(jī)變量的期望   4.2 期望的性質(zhì)   4.3 方差   4.4 矩   4.5 均值和中位數(shù)   4.6 協(xié)方差和相關(guān)系數(shù)   4.7 樣本均值   4.8 補(bǔ)充練習(xí) 5 特殊分布   5.1 引言   5.2 伯努利和二項(xiàng)分布   5.3 超幾何分布   5.4 泊松分布   5.5 正態(tài)分布   5.6 中心極限定理   5.7 伽馬分布   5.8 貝塔分布   5.9 二元正態(tài)分布   5.10 補(bǔ)充練習(xí) 6 估計(jì)   6.1 統(tǒng)計(jì)推斷   6.2 最大似然估計(jì)   6.3 最大似然估計(jì)的性質(zhì)   6.4 補(bǔ)充練習(xí) 7 估計(jì)量的抽樣分布   7.1 統(tǒng)計(jì)量的抽樣分布   7.2 卡方分布   7.3 樣本均值和方差的聯(lián)合分布   7.4 t分布   7.5 置信區(qū)間   7.6 無偏估計(jì)   7.7 補(bǔ)充練習(xí) 8 假設(shè)檢驗(yàn)   8.1 假設(shè)檢驗(yàn)的問題   8.2 t檢驗(yàn)   8.3 兩個(gè)正態(tài)分布均值的檢驗(yàn)   8.4 F分布   8.5 補(bǔ)充練習(xí) 9 屬性數(shù)據(jù)和非參數(shù)方法   9.1 擬合優(yōu)度檢驗(yàn)   9.2 復(fù)合假設(shè)的擬合優(yōu)度檢驗(yàn)   9.3 補(bǔ)充練習(xí) 10 線性統(tǒng)計(jì)模型   10.1 最小二乘法   10.2 回歸   1O.3 簡(jiǎn)單線性回歸的統(tǒng)計(jì)推斷   10.4 補(bǔ)充練習(xí) 統(tǒng)計(jì)表 部分習(xí)題答案 參考文獻(xiàn) 中英文詞匯表

章節(jié)摘錄

　　The concepts of chance and uncertainty are as old as civilization itself.People havealways had to cope with uncertainty about the weather，their food supply，and other as-pects of their environment，and have striven to reduce this uncertainty and its effects.Eventhe idea of gambling has a long history.By about the year 3500 B.C..games of chanceplayed with bone objects that could be considered precursors of dice were apparentlyhighly developed in Egypt and elsewhere.Cubical dice with markings virtually identi-cal to those on modern dice have been found in Egyptian tombs dating from 2000 B.C.We know that gambling with dice has been popular ever since that time and played animportant part in the early development of probability theory.　　It iS generally believed that the mathematical theory of probability was started by theFrench mathematicians Blaise Pascal（1623-1662）and Pierre Fermat（601－1665）whenthey succeeded in deriving exact probabilities for certain gambling problems involvingdice.Some of the problems that they solved had been outstanding for about 300 years.However.numerical probabilities of various dice combinations had been calculated pre-viously bv Girolamo Cardano（1501－1 576）and Galileo Galilei（1564－1642）.　　The theory of probability has been developed steadily since the seventeenth centuryand has been widely applied in diverse fields of study.Today.probability theory iS animportant toolin most areas of engineering.science.and management.Many researchworkers are actively engaged in the discovery and establishment of new applications ofprobability in fields such as medicine，meteorology，photography from satellites，mar-keting，earthquake prediction，human behavior，the design of computer systems，finance，genetics.and law.In many legal proceedings involving antitrust violations or employmentdiscrimination.both sides will present probability and statistical calculations to help sup-port their cases.

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