搜索
毕业论文题目数学期望的计算方法及应用学院数学科学学院专业数学与应用数学班级数学0902学生邴孝臣学号20090921004指导教师韩雪二〇一三年五月二十五日济南大学毕业论文-I-摘要概率论与数理统计是数学中一条非常重要的分支，同时数学期望也是概率统计中非常重要的一部分.随着中国改革开放以来的快速发展，概率统计在我国社会主义事业建设中的应用越来越多，其中数学期望的应用理所当然的占据了一席之地.本文以数学期望的定义及性质为基础，以数学期望的计算方法为指导，通过对相关资料的深入学习并进行归纳总结.系统全面的论述了三种类型的数学期望，以及相应的计算方法和广泛的应用，为人们更好的掌握数学期望打下了基础.其中在应用部分包括数学期望在保险、等候电梯、商业、公交车、管理、系统寿命、医学普查、个人投资等多个领域的应用.重点论述了在系统寿命中的应用，其中包含多种系统.为人们更好的生活奠定了基石，也为我国的经济又好又快发展提供了理论指导.关键词：数学期望；计算方法；应用；系统寿命ABSTRACTProbabilitytheoryandmathematicalstatisticsisaveryimportantbranchof济南大学毕业论文-II-mathematics,themathematicalexpectationisaveryimportantpartinprobabilityandstatistics.WiththerapiddevelopmentofChina'sreformandopeningup,probabilityandstatisticsisusedmoreandmoreinthecauseofsocialistconstructioninChina,includingtheapplicationofmathematicalexpectationbehooveoccupyaspaceforoneperson.Basedonthedefinitionandpropertiesofthemathematicalexpectation,methodtocalculatemathematicalexpectationastheguide,throughin-depthstudyontherelateddataandsummary.Acomprehensivesystemofthemathematicalexpectationofthreetypes,andthecorrespondingcalculationmethodandappliedwidely,forpeopletobettergraspthemathematicalexpectationandlaythefoundation.Applicationofmathematicalexpectationforapluralityoffieldofelevators,business,management,systembus,life,medicalscreening,personalinvestmentintheinsurance,whichinthepartofapplicationincluding.Thisarticlefocusesontheapplicationofthesysteminthelife,whichcontainsavarietyofsystem.Andlaidthefoundationforabetterlife,butalsoprovidestheoreticalguidanceforChina'seconomicdevelopment.Keywords：mathematicalexpectation;calculationmethod;application;systemlife目录摘要.............................................................................................................................IABSTRACT...........................................................................................................................I济南大学毕业论文-III-1前言...................................................................................................................................11.1研究的目的与意义.................................................................................................11.2研究的背景.............................................................................................................12数学期望的定义及性质...................................................................................................22.1离散型随机变量的数学期望.................................................................................22.2连续型随机变量的数学期望.................................................................................22.3一般随机变量的数学期望.....................................................................................32.4数学期望的性质.....................................................................................................53数学期望的计算方法........................................................................................................83.1离散型随机变量的数学期望的计算方法.............................................................83.1.1用定义求之....................................................................................................83.1.2利用常见离散型随机变量的数字特征公式求之........................................93.1.3随机变量分解法............................................................................................93.2连续型随机变量的数学期望的求法...................................................................103.2.1根据定义求之.............................................................................................103.2.2已知分布函数，可先求概率密度，再按定义式求其数学期望；但也可根据下式直接求出...................................................................................................113.2.3利用数学期望的的性质求之.....................................................................123.2.4利用连续型随机变量的数字特征求之.....................................................133.2.5利用分布的对称性求之..............................................................................134数学期望的应用..............................................................................................................144.1数学期望在保险公司中的应用............................................................................144.2数学期望在大学生等候电梯中的应用................................................................144.3数学期望在商店进货中的应用............................................................................154.4数学期望在公交车上的应用................................................................................164.5数学期望在风险型决策中的具体应用................................................................164.6数学期望在系统寿命中的应用............................................................................184.7数学期望在医学疾病普查中的应用....................................................................224.8数学期望在个人投资中的应用............................................................................23结论.............................................................................................................................25参考文献.......................................................................................................................26致谢........................................................