【正文】 東?？茖W技術(shù)學院畢業(yè)論文 I 正態(tài)分布的發(fā)展 及應(yīng)用 摘 要 生活中諸多的經(jīng)驗和理論都表明，我們所處的環(huán)境中服從正態(tài)分布的事件是極其常見的。例如：工程中的加工尺寸，人的 身 高，降雨量等都可以看做是正態(tài)分布。所以在統(tǒng)計學中對于正態(tài)分布的使用越來越廣泛。本文是對正態(tài)分布的發(fā)展以及應(yīng)用做一些基本的闡述。 正態(tài)分布又 名 高斯分布， 德國 數(shù)學家高斯對于正態(tài)分布的形成 與發(fā)展有 著 舉足輕重的地位 。正態(tài)分布從無到有，最后成為數(shù)理統(tǒng)計中非常重要的模型 大致可分為三個階段：第一個階段是形成階段， 18 世紀 30 年代數(shù)學家狄莫弗在一個賭博問題的概率計算中 意外 發(fā)現(xiàn)了正態(tài)曲 線，所以人們也把 正 態(tài)分布的起源歸于賭博問題 ，但由于社會及個人的問題，正態(tài)曲線在那時并沒都得到很大的發(fā)展。第二個階段 是 18 世紀中葉 正態(tài)分布的模型建立， 在天文學發(fā)展的刺激下， 數(shù)學家拉普拉斯， 高斯 對于正態(tài)分布又有了新的拓展 ，讓人們逐漸認識到了其在天文，誤差領(lǐng)域的應(yīng)用。第三階段 19 世紀中葉在凱特萊， 高爾頓 的努力下，使正態(tài)分布進入到自然和科學領(lǐng)域 ，從此進入了統(tǒng)計學的大家庭。 最后本文總結(jié)了現(xiàn)階段正態(tài)分布的一些最基本最實用的應(yīng)用。 【關(guān)鍵詞】 正態(tài)分布 狄莫弗 拉普拉斯 高斯 凱特萊 東?？茖W技術(shù)學院畢業(yè)論文 II Development and Application of the Normal Distribution Fengjie xue (Department of mathematics physics and information, Donghai Science amp。 Technology School 316004) Abstract Many life experiences and theories that we normally distributed environment in which the event is extremely mon. For example: the size of the project in the process, a person’s height, rainfall and so can be seen as a normal distribution. Therefore, the normal distribution in statistics more widely used. This article is a normal development and application to do some basic exposition. Normal distribution, also known as the Gaussian distribution, the German mathematician Gauss for the formation and development of the normal distribution has a pivotal position. Normal distribution from scratch, eventually became a very important mathematical statistics model can be divided into three stages: the first stage is the formation stage, 18 in the 1930s mathematician Moivre probability calculations in a gambling problem accidentally discovered normal curve, so people have attributed the origin of the normal distribution of gambling problems, but because of social and personal problems, the normal curve at that time did not have a great development. The second stage is the mid18th century the normal distribution model, the stimulation of the development of astronomy, mathematician Laplace, Gaussian normal distribution has a new development, so that people e to realize that its in astronomy, application error field. The third stage in the mid19th century Quetelet, Galton’s efforts to make the normal into the natural and scientific fields, from entering the family statistics. Finally, the paper summarizes some of the most basic and normal stage of practical application.【 Keywords】 Normal distribution Moivre Laplace Gauss Kettle 東?？茖W技術(shù)學院畢業(yè)論文 III 目 錄 摘 要 ............................................................................................................................... I Abstract............................................................................................................................. II 1 緒論 .............................................................................................................................1 正態(tài)分布的定義 .................................................................................................1 正態(tài)分布的曲線 ..................................................................................................1 正態(tài)分布與標準正態(tài)分布 ..................................................................................2 ...........................................................................................................3 2． 1 古典統(tǒng)計時期的概率論 ..................................................................................3 2． 2 二項式正態(tài)逼近 —— 狄莫弗 ..........................................................................4 2． 3 為何當時正態(tài)分布未能有大發(fā)展 ..................................................................4 ...................................................................................................6 3． 1 天文中的誤差 ..................................................................................................6 3． 2 誤 差論的形成 ..................................................................................................6 3． 2． 1 拉普拉斯的概率論