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《随机规划-姚凯》ProbabilityTheory.pdf

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《随机规划-姚凯》ProbabilityTheory.pdf

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文档介绍:UTLogo100Stochastic ProgrammingSchool of Management, UCASV??Dú?p¥I?????+n??Kai ******@ ProgrammingSchool of Management, UCASV??Y?:?8,A:σ-?ê,A∈A:ˉ???úúúnnn1.(555???555)é?8?§kPr{?}= 1"úúúnnn2.(???KKK555)é??ˉ?A§kPr{A} ≥0"úúúnnn3.(?????????\\\555)é?????ˉ?{Ai}§kPr(∞[i=1Ai)=∞Xi=1Pr{Ai}.n?|(?,A,Pr)??V??m"Kai ******@ ProgrammingSchool of Management, UCAS~1é?qM1§?={?§?}§??Pr{?}=Pr{?}= ,Pr{?}= 0,Pr{?}= 1,KPr′??V??Y§(?,A,Pr)′??V??m"~2??={ω1, ω2, ω3}§d?A??k8?ˉ?"??Pr{ω1}= ,Pr{ω2}= ,Pr{ω3}= ,Pr{ω1, ω2}= ,Pr{ω1, ω3}= ,Pr{ω2, ω3}= ,Pr{?}= 0,Pr{?}= 1,KPr′??V??Y§(?,A,Pr)′??V??m"Kai ******@ ProgrammingSchool of Management, UCAS??Ct???ξ′lV??m(?,A,Pr)?¢ê8<????ê,XJéu???Borel8B,8ü{ξ∈B}={ω∈?|ξ(ω)∈B}′??ˉ?,K?ξ′????Ct.??t§??Ct′lV??m?¢ê8??????N?"Kai ******@ ProgrammingSchool of Management, UCAS~3éu~1¥?V??m§?êξ{?}= 1, ξ{?}=?1,Kξ′????Ct§d?Pr{ξ= 1}= ,Pr{ξ=?1}= .~4é~2¥???V??m,?êξ(ω) =????1,XJω=ω10,XJω=ω21,XJω=ω3′???? ******@ ProgrammingSchool of Management, UCASV??ù???ξ′????Ct,K?êΦ(x) =Pr{ξ≤x}=Pr{ω∈?|ξ(ω)≤x}??ξ?£\è¤V??ù.XJ?êΦ???êφ3,***@oφ??ξ?V??Y?ê.Kai ******@ ProgrammingSchool of Management, UCAS~5éu~1ú~3¥?????Ct?\èV??ù′Φ(x) =???0,XJx<?,XJ?1≤x<11,XJx≥1.??μéu~2ú~4¥?????Ct?\èV??ù′?ooKai ******@ ProgrammingSchool of Management, UCAS~?V??ù-I??|?ùPr{ξ= 1}=p,Pr{ξ= 0}= 1?p???ùPr{ξ=k}=Cknpk(1?p)n?kA??ùPr{ξ=k}=p(1?p)k?1?t?ùPr{ξ=k}=λkk!exp(?λ)Kai ******@ ProgrammingSchool of Management, UCAS~?V??ù-II?ù??Y?êV??ùt!?ùφ(x) =1b?aΦ(x) =x?ab?a?ê?ùφ(x) =λexp(?λx) Φ(x) = 1?exp(?λx)???ùφ(x) =1√2πσexp??(x?μ)22σ2?éê???ùφ(x) =1√2πσxexp??(lnx?μ)22σ2?Kai ******@ ProgrammingSchool of Management, UCAS$?{K?n?ξ1, ξ2,· · ·, ξn′V??m(?,A,Pr)t?????Ct,f′??n????ê"??ξ(ω) =f(ξ1(ω), ξ2(ω),· · ·, ξn(ω)),***@oξ?′V??m(?,A,Pr)t?????Ct"~X,eξ1