文档介绍：该【数学实验概率论与数理统计分册习题1 】是由【liaoyumen】上传分享，文档一共【15】页，该文档可以免费在线阅读，需要了解更多关于【数学实验概率论与数理统计分册习题1 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured14severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured15severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,,具有一定难度。这种考试包括听力、语法结构、阅读理解、写作等。除写作占15分外,其余85道为单项选择题,每道题附有A、B、C、D四个选项。这种考试方法使个别学生产生碰运气和侥幸心理,那么,靠运气能通过英语四级考试吗?解:假设学生作文得满分,即15分,85道选择题每道题都靠蒙,即每道题做对的概率为1/4,得60分则通过考试。则该同学通过考试的概率为:P=>>nchoosek(85,40)*(1/4)^45*(3/4)^40ans=-008即:由此可见,即使该同学作文满分,靠运气通过考试的概率也是如此的低,所以可以认为靠运气不能通过英语四级考试。={(x,y)|(x,y)∈Q,x2+y2≤1},Q={(x,y)|0≤x≤1,0≤y≤1}上考虑计算二重积分(利用Monte-carlo法):severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured2severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured15severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured解:积分区域如右图所示:>>n=10000;%模拟次数x=rand(n,1);%点的x坐标y=rand(n,1);%点的y坐标m=sum(sin(x+y)./(x+y)&x.^2+y.^2<=1);Vn=m/n%落到所求面积内的点的频率,即概率的模拟值Vn=,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured14severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured3severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,。根据统计资料,成年男子的身高X服从均值为168厘米,方差为7厘米的正态分布,那么车门的高度应该至少设计为多少厘米?解:>>norminv(,168,7)ans=,各仪器工作相互独立,,通常一台仪器的故障由一人即可排除。试问:(1)为保证当仪器发生故障时,,至少要配多少个维修工人?(2)若一人包修20台仪器,仪器发生故障时不能及时排除的概率是多少?(3)若由3人共同负责维修80台仪器,仪器发生故障时不能及时排除的概率是多少?解:(1)设X表示300台仪器中发生故障的台数,则XB(300,),设b为需要配备的维修工人数,则应有P{X>b}≤,即,由于n=300较大,p=,根据泊松定理,可以用λ=np=3的泊松分布近似计算。用Matlab计算:>>poissinv(,3)ans=severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured4severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured15severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured8所以为达到要求至少需配备8名维修工人。???????(2)设Y表示20台仪器中发生故障的台数,则Y~B(20,)。若在同一时刻发生故障的仪器数Y≥2,则一个工人不能维修,此概率为,用Matlab计算:>>1-^20-nchoosek(20,1)**^19ans=。(3)设Z表示80台仪器中发生故障的台数,则Z~B(80,)。若在同一时刻发生故障的仪器数Z≥4,则由三个工人共同负责保修时不能及时维修,此概率为用Matlab计算:>>1-^80-nchoosek(80,1)**^79-nchoosek(80,2)*^2*^78-nchoosek(80,3)*^3*^77ans=。severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured14severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured5severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,,在众多因素的影响下包装封口后一袋的重量是随机变量,设其服从正态分布N(m,b2),其中b已知,m可以在包装时调整,出厂检验时精确地称量每袋重量,多余500克的仍按500克一袋出售,因而厂家吃亏;不足500克的降价处理,或打开封口返工,或直接报废,这样厂方损失更大,问如何调整m的值使得厂方损失最小?解:假设b=1【实验方案】,依题意x为一随机变量,且服从正态分布N(m,b2),概率密度函数为:,(-∞<x<+∞),b>0为已知,m待定。当成品重量M给定后,记:P=P(x≥M)=P’=P(x<M)=故而有:P+P’=1由以上分析,可将上式的第一项作为目标函数J(m):J(m)=,P(m)表示概率P=P(x≥M)是m的函数分析题意可知,厂方损失Y由两部分组成:(1)x≥L时,多余部分,重量为(x-L);(2)x<L时,整袋报废,重量为x;Y==m-,所以生产N袋糖果,得到NP袋成品,损失总重量为(mN-MNP),因此每得到一袋成品所损失糖果的平均重量J1为:severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured6severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured15severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasuredJ1=(m)的最小值点即可。:设F(x)为正态分布N(m,b2)的分布函数,Φ(x)为标准正态分布的分布函数,则,J(m)===令c=,d=,z=d-c则上式可简化为:J(z)=【实验过程】::functionJ=Jmin(m)J=m/(1-normcdf((500-m),0,1));::form=5000::510J=Jmin(m);plot(m,J)holdonend运行结果为:severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured14severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured7severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured从目标函数的图形可以看出,函数在500到505内取得最小值,而且当自变量向500逼近时,函数图像值急剧上升,自变量从503开始以后,函数图像接近于一条直线。::min=600;minm=0;form=500::530J=Jmin(m);ifJ<=minmin=J;minm=m;endseveralgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured8severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured15severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasuredendwasteaverage=min-500;minm,min,wasteaverage运行后运行结果为:minm====,目标函数值最小,,此时,生产一袋成品所损失糖果的平均重量J1=。severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured14severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,listcanmeasured9severalgroupnumber,thenwithb±a,=c,-2~3measurement,suchasproceedsofcvaluesareequalandequaltothedesignvalue,,b,andcvalueswhileonhorizontalverticalerrorsformeasurement,Generalinironanglecodebitatmeasurementlevelpointsgriderrors,omethylverticalboxcenterlinedistancefora,,tobverticalboxdistanceforb,,2,…,9号码的9只球放在一个盒子中,从其中有放回地取出4只球,重复取100次,求所得号码之和X的数学期望及其方差。解:在MATLAB命令窗口输入:>>n=100;sele=[];forii=1:nsort=randperm(9);sele(:,ii)=sort(1:4);endsigma=sum(sele);Ex=mean(sigma),Dx=var(sigma)输出结果为:Ex==