數(shù)學畢業(yè)論文切比雪夫不等式的推廣與應用

1、數(shù)學畢業(yè)論文-切比雪夫不等式的推廣與應用  切比雪夫不等式的推廣與應用摘要：在估計某些事件的概率的上下界時，常用到著名的切比雪夫不等式.本文從4個方面對切比雪夫不等式進行推廣，討論了切比雪夫不等式在8個方面的應用，并證明了隨機變量序列服從大數(shù)定理的1個充分條件.最后給出了切比雪夫不等式其等號成立的充要條件，并用現(xiàn)代概率方法重新證明了切比雪夫不等式.關鍵詞：切比雪夫不等式；隨機變量序列；強大數(shù)定理；幾乎處處收斂；大數(shù)定理.              

2、;         the popularization and application of chebyster’s inequalityabstract:the famous chebyshev’s inequality is usually used when estimating the boundary from above or below of probability . the paper presents popularization from four respects.

3、 first, the paper discusses its application in eight aspects and demonstrates a complete condition that the foundation of random number sequence coconforms to he law of large numbers  theorem. and then , the author analyzes its complete and necessary condition for foundation of chebyshev’

4、s ineuquality. furthermore, the paper makes a demonstration again for chebyshev’s inequality with the method of modern probability.key words: cherbyshev’ inequality; random number sequence; law of large numbers; almost everywhere convergence；law of strong large numbers.目錄中文標題…&hel

5、lip;………………………………………………………………………………………1中文摘要、關鍵詞……&hellip

6、;…………………………………………………………………………1英文標題……………………&helli

7、p;……………………………………………………………………1英文摘要、關鍵詞…………………………&

8、hellip;……………………………………………………1正文§1 引言………………………………………

9、……………………………………………………2§2切比雪夫不等式的推廣 ………………………………………&

10、hellip;……………………………2§3切比雪夫不等式的應用 ……………………………………………………………&h

11、ellip;………53.1 利用切比雪夫不等式說明方差的意義………………………………………………………53.2 估計事件的概率……………………&hell

12、ip;………………………………………………………53.3  說明隨機變量取值偏離ex超過3 的概率很小 ………………………………

13、……………73.4 求解或證明有關概率不等式…………………………………………………………………73.5 求隨機變量序列依概率的收斂值………

14、……………………………………………………93.6 證明大數(shù)定理…………………………………………&

15、hellip;……………………………………113.7 證明強大數(shù)定理………………………………………………………

16、………………………123.8 證明隨機變量服從大數(shù)定理的1個充分條件………………………………………………20§4切比雪夫不等式等號成立的充要條件 …………&

17、hellip;…………………………………………22§5 結束語…………………………………………………

18、………………………………………25參考文獻……………………………………………………………………………………………26致謝………………………&hell