目錄
第一章：緒論------------------------------------------------------------------- 3
1.1 隨機(jī)變量------------------------------------------------------------------------------3
1.2 離散型隨機(jī)變量及其分布---------------------------------------------------------3
1.3 連續(xù)型隨機(jī)變量及其分布---------------------------------------------------------4
第二章：常見離散型分布及其應(yīng)用-----------------------------------------4
2.1 0-1分布及其應(yīng)用---------------------------------------------------------------- ----4
2.2 幾何分布及其應(yīng)用-------------------------------------------------------------------5
2.3 二項(xiàng)分布及其應(yīng)用-------------------------------------------------------------------6
2.4 泊松分布及其應(yīng)用-------------------------------------------------------------------7
第三章：常見連續(xù)型分布及其應(yīng)用-----------------------------------------11
3.1 均勻分布及其應(yīng)用-----------------------------------------------------------------11
3.2 指數(shù)分布及其應(yīng)用-----------------------------------------------------------------12
3.3 正態(tài)分布及其應(yīng)用-----------------------------------------------------------------13
參考文獻(xiàn)------------------------------------------------------------------------23










常見分布的性質(zhì)及其應(yīng)用

張久恩，數(shù)學(xué)計(jì)算機(jī)學(xué)院

摘 要：在概率論領(lǐng)域里，我們研究的概率分布大體分為兩種：離散型概率分布和連續(xù)性概率分布。常見的離散型的概率分布有四種--兩點(diǎn)分布或（0-1）分布， 幾何分布，二項(xiàng)分布以及泊松分布。而常見的連續(xù)性概率分布有三種--均勻分布，指數(shù)分布，正態(tài)分布。這七種常見的概率分布使我們學(xué)習(xí)概率論的最基本最常見的分布。而這七種分布之間也有相互的聯(lián)系。兩點(diǎn)分布即是一種特殊的二項(xiàng)分布；二項(xiàng)分布在n趨向 時近似泊松分布；泊松分布和二項(xiàng)分布在n趨向 時也服從正態(tài)分布。這七種概率分布因其基礎(chǔ)性與常見性，因而在實(shí)際生活中應(yīng)用廣泛，特別是工程，醫(yī)藥，財(cái)經(jīng)等領(lǐng)域。
本文先是介紹了一些基本的概率知識，用集合的方法定義一些概率的概念。然后介紹兩大類概念分布--離散型概率分布和連續(xù)性概率分布。緊接著著重學(xué)習(xí)研究了上面提到的七種概率分布：（0-1）分布，幾何分布，二項(xiàng)分布，泊松分布，均勻分布，指數(shù)分布，正態(tài)分布及其應(yīng)用。而正態(tài)分布又是我們最為常見研究最多應(yīng)用最為廣泛的概率分布。

關(guān)鍵詞：離散型概率分布；連續(xù)性概率分布；(0-1）分布；幾何分布；二項(xiàng)分布；泊松分布；均勻分布；指數(shù)分布；正態(tài)分布；





The quality and application of common probability distribution

ZhangJiuEn，Mathematics and applied mathematics


Abstract： The distributions which we study in the fields of possibility apparently classify as two rates: The discrete distribution and continuous distribution. While two-points distribution or (0-1) distribution, geometric distribution, binominal distribution and poisson distribution are the common four kinds of discrete distributions. And the uniform distribution ,exponential distribution and normal distribution are the common three kinds of continuous distributions .These seven types of distributions are the most basic and common distribution we have learned. What’s more ,there is some relation among these distributions. For instance, two-points distribution is a special type of binomial distribution; and binomial distribution similar to poisson distribution when n tends to ; besides, poisson and binomial distribution similar to the normal distribution when n tends to . These seven kinds of distribution are applied widely in the daily life, especially in the fields of engineering and medicine and finance, due to their fundamental and common quality.
We introduce some basic knowledges of possibility firstly, define some concepts of possibility with the methods of set. And then we introduce the two types of possibility distribution—discrete distribution and continuous distribution. Lastly, we focus on the study of the seven kinds of distributions discussed above. And the normal distribution is the distribution we study and applied mostly,and also the most commom one.
Key words : Discrete Distribution；Continuous Distribution; Two-points Distribution; Geometric Distribution; Binomial Distribution; Poisson Distribution; Uniform Distribution; Exponential Distribution; Normal Distribution.