概率统计第三章 多维随机变量及其分布

为搞好山东省交通科学研究所研发基地项目的结算审计工作,我跟踪审计部特针对本项目作如下要求,请各施工单位、供货单位遵照执行：andperformancetestcopiesoftherecord.Ifnecessary,reviewshouldbecarriedout;4)forspringhangers(includedsimplespring,hangersandconstantsupporthangers)itshouldalsoberecognizedassettingandlockingofloads.5)checkthesurfacequality,foldedlayeringandwithoutcracks,rustandotherdefects.5)aftercompletionofthetestandcontroldrawingnumberonebyone,byseriesbaled.Coloralloysteelparts,thepartsmarkinginstallationlocationandrotationaboutthedirectionyouwant.7.3.14.hangersinstallation7.3.14.1hangerlayouta.acleardesignofhangershouldbeinstalledstrictlyinaccordancewiththedrawingsanddesignsshallnotbeinstalledwrong,missing,etc.B.ownarrangementofpipingsupportandhangersetandselectionshouldbebasedoncomprehensiveanalysisofgenerallayoutofpipingsystems;coldinstallationofsteampipewithparticularattentionreservedforcompensationofthermalexpansiondisplacementandorientation.C.supportsystemsshouldberationaltowithstandpipeloads,staticloadandincidentalload;reasonablepipingdisplacement;guaranteedundervariousconditions,stressarewithintheallowedrange.Strength,stiffness,andmeetrequirementstopreventvibrationandsoothingwater,withoutaffectingtheadjacentequipmentmaintenanceandotherpipinginstallationandexpansion.D.equipmentconnectedtotheinterfacetomeetpipelinethrust(torque)limitrequirements;increasethestabilityofpipingsystemstopreventpipeline...Tubewallthickness(mm)2-34-67-10weldformnoslopemouthweldstrengtheningheighth(mm)1-1.51.5-2weldwidthb(mm)5-67-6hasslopemouthweldstrengtheningheighth(mm)1.5-22weldwidthb(mm)coverhadeachedgeslopemouthabout2mmargonarcweldingweldstrengtheningsurfaceheightandwidthtubewallthickness(mm)2--33--45--6weldformweldstrengtheningheighth(mm)1-1.51.5-22-2.5widthb(mm)第三章多维随机变量及其分布上次课复习：概率论实践中总结出了重要的几类概率模型和与之相关的随机变量的概率分布：二项分布，泊松分布，均匀分布，正态分布等．我们需要了解这些重要的概率分布及其产生的背景，从而指导决策．教材章节题目：第三章多维随机变量及其分布第一节多维随机变量及其分布（§3.1§3.2）教学要求：了解多维随机变量的概念．了解二维随机变量的联合分布函数的概念和性质．理解二维离散型随机变量的联合分布律的概念和性质，二维连续型随机变量的联合密度函数的概念和性质．了解二维均匀分布、二维正态分布．掌握由二维随机变量的联合分布求边缘分布重点：联合分布律，联合密度函数，边缘分布难点：由联合分布求边缘分布教学手段及教具：板书，多媒体讲授内容及时间分配：二维随机变量及其分布函数20分钟二维离散型随机变量的分布律25分钟二维连续型随机变量的概率密度函数45分钟由联合分布确定边缘分布45分钟课后作业习题三1~6参考资料《概率论与数理统计》盛骤等编著高等教育出版社《概率论与数理统计》陈希孺编著科学出版社《AFirstCourseinProbability》RossSM著PearsonEducation,Inc.为搞好山东省交通科学研究所研发基地项目的结算审计工作,我跟踪审计部特针对本项目作如下要求,请各施工单位、供货单位遵照执行：andperformancetestcopiesoftherecord.Ifnecessary,reviewshouldbecarriedout;4)forspringhangers(includedsimplespring,hangersandconstantsupporthangers)itshouldalsoberecognizedassettingandlockingofloads.5)checkthesurfacequality,foldedlayeringandwithoutcracks,rustandotherdefects.5)aftercompletionofthetestandcontroldrawingnumberonebyone,byseriesbaled.Coloralloysteelparts,thepartsmarkinginstallationlocationandrotationaboutthedirectionyouwant.7.3.14.hangersinstallation7.3.14.1hangerlayouta.acleardesignofhangershouldbeinstalledstrictlyinaccordancewiththedrawingsanddesignsshallnotbeinstalledwrong,missing,etc.B.ownarrangementofpipingsupportandhangersetandselectionshouldbebasedoncomprehensiveanalysisofgenerallayoutofpipingsystems;coldinstallationofsteampipewithparticularattentionreservedforcompensationofthermalexpansiondisplacementandorientation.C.supportsystemsshouldberationaltowithstandpipeloads,staticloadandincidentalload;reasonablepipingdisplacement;guaranteedundervariousconditions,stressarewithintheallowedrange.Strength,stiffness,andmeetrequirementstopreventvibrationandsoothingwater,withoutaffectingtheadjacentequipmentmaintenanceandotherpipinginstallationandexpansion.D.equipmentconnectedtotheinterfacetomeetpipelinethrust(torque)limitrequirements;increasethestabilityofpipingsystemstopreventpipeline...Tubewallthickness(mm)2-34-67-10weldformnoslopemouthweldstrengtheningheighth(mm)1-1.51.5-2weldwidthb(mm)5-67-6hasslopemouthweldstrengtheningheighth(mm)1.5-22weldwidthb(mm)coverhadeachedgeslopemouthabout2mmargonarcweldingweldstrengtheningsurfaceheightandwidthtubewallthickness(mm)2--33--45--6weldformweldstrengtheningheighth(mm)1-1.51.5-22-2.5widthb(mm)第三章多维随机变量及其分布第一节多维随机变量及其分布５．二维随机变量若对于试验的样本空间中的每个试验结果e，有序变量(,)XY都有确定的一对实数值与e相对应，即()XXe，()YYe，则称(,)XY为二维随机变量或二维随机向量．6．二维离散型随机变量及联合概率函数如果二维随机变量(,)XY仅可能取有限个或可列无限个值，那么，称(,)XY为二维离散型随机变量．二维离散型随机变量(,)XY的分布可用下列联合概率函数来表示：(,),,1,2,,ijijPXaYbpij其中，0,,1,2,,1ijijijpijp．7．二维离散型随机变量的边缘概率函数设(,)XY为二维离散型随机变量，ijp为其联合概率函数（,1,2,ij），称概率()(1,2,)iPXai为随机变量X的边缘概率函数，记为ip并有.(),1,2,iiijjpPXapi，称概率()(1,2,)jPYbj为随机变量Y的边缘概率函数，记为.jp，并有.jp=(),1,2,jijiPYbpj.8．随机变量的相互独立性．设(,)XY为二维离散型随机变量，X与Y相互独立的充分必要条件为,,1,2,.ijijpppij对一切多维随机变量的相互独立性可类似定义．即多维离散型随机变量的独立性有与二维相应的结论．９．二维离散型随机变量(,)XY的条件概率函数设(,)XY为二维离散型随机变量，ijp为其联合概率函数(,1,2,)ij，X在给定jYb下的条件概率函数为(|),1,2,;ijijjpPXaYbipY在给定iXa下的条件概率函数为(|),1,2,ijjiipPYbXajp10．随机变量函数的分布设X是一个随机变量，()gx是一个已知函数，()YgX是随机变量X的函数，它也是一个随机变量．对离散型随机变量X，下面来求这个新的随机变量Y的分布．设离散型随机变量X的概率函数为为搞好山东省交通科学研究所研发基地项目的结算审计工作,我跟踪审计部特针对本项目作如下要求,请各施工单位、供货单位遵照执行：andperformancetestcopiesoftherecord.Ifnecessary,reviewshouldbecarriedout;4)forspringhangers(includedsimplespring,hangersandconstantsupporthangers)itshouldalsoberecognizedasse