隨機(jī)變量的獨(dú)立性
Independence of random variables



摘要 隨機(jī)變量的獨(dú)立性是概率論中最基本的概念之一,研究隨機(jī)變量的獨(dú)立性可以使得很多實(shí)際問題的具體計(jì)算得以簡(jiǎn)化.本文首先介紹了隨機(jī)變量獨(dú)立性的定義.然后對(duì)離散型隨機(jī)變量以及連續(xù)型隨機(jī)變量的獨(dú)立性分別給出了兩種判別的方法,同時(shí)得出了一系列相關(guān)的推論,并且對(duì)于其應(yīng)用進(jìn)行了舉例說明.最后這篇文章對(duì)于隨機(jī)變量的獨(dú)立性在求隨機(jī)變量特征數(shù)中的一些應(yīng)用進(jìn)行了整合.

Abstract
The independence of the random variable is the most basic concept of probability. The study of it can make many specific calculations of the practical problems easier. First of all, this paper introduces the definition of the independence of random variables. Secondly, for the independence of discrete random variables and continuous random variables, the article gives two judgmental methods to them, and obtains some inferences; this paper also illustrates some examples for these applications. At last, this paper composes some applications of the independence of the random variable for the calculation of some random variable numeral characters.

關(guān)鍵詞:離散型隨機(jī)變量;連續(xù)型隨機(jī)變量;獨(dú)立性;數(shù)學(xué)期望;方差

Key words: discrete random variable; continuous random variable; independence; mathematical expectation; variance
目 錄

1 引言 1
2 隨機(jī)變量獨(dú)立性的定義 1
3 隨機(jī)變量獨(dú)立性的判定 2
3.1 離散型隨機(jī)變量獨(dú)立性的判定 2
3.1.1 判別方法一 2
3.1.2 判別方法二 5
3.2 連續(xù)型隨機(jī)變量獨(dú)立性的判定 8
3.2.1 判別方法一 8
3.2.2 判別方法二 9
4 隨機(jī)變量獨(dú)立性與數(shù)字特征 11
4.1 隨機(jī)變量獨(dú)立性與數(shù)學(xué)期望 12
4.2 隨機(jī)變量獨(dú)立性與方差 12
4.3 隨機(jī)變量獨(dú)立性與協(xié)方差 13
4.4 隨機(jī)變量獨(dú)立性與相關(guān)系數(shù) 13
總結(jié) 14
參考文獻(xiàn) 15
致 謝 16