А.А. Кудрявцев - Пособие по теории вероятностей (1115312)
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. , ω n]^bRTRaD5]PIv_JQHdQ ~FHGHIQstWNjm*NPOHQHNX]PIAv_JQHBdQ ~A BFHGHIQstWNjm*NPOHQHNX]PIv_JQHdQ ~G=DstOHI]^Jlz]PIv_JQHdQ A~ BOHNPWI&stRTILM9OHIN]PIv_JAQHN&~ B]PIv_JQHN&nHm*IFHI\*OHQJNj\*lOHINXYu]PIv_JQHf~AWNPGHILKJOHI]^Jl9]PIv_JQK ~RTI&iOHI]^JlzRTOHIMNP]^JW.D A ~kHQH]j\*Iz]PIkHN^JD&OHQHd+Qs AFHI h k~nk Cn = n!/(k!(n − k)!)ZXD&YJIGHQ=D\+kHQH]j\D h~n n! = 1 · 2 · . . . · nUPNPIRTN^JGHQHkHNP]tYDKuRaN^G=DÕmH\*QHO=DnHF\*I&iDm*lHn=Iv&¹NPR RTOHIoMNP]^JW.D ~b.]j\*IWO=DGKWNPGHILKJOHI]^Jlq]PIv_JQKFHGHQb]j\*IWQHQn¦kJIAFHGHIQstI&pX\*Iz]PIv_JQHN ~WNPGHIKJOHI]^JlqFHILKHW\*NPOHBQKºb]PFHNjVIW"W+]eV.NPRTNOHN^sLDoknWQH]PQHRT_:VuQH]PFH_JD&OHQHd) :NPGHObt\H\*Q~WN^GHIKJOHI]^Jl5FHIKHW\*N^OHQKyOHNRTNPOHNPN ºb]PFHNjV.IWW]rV.NPRTNOHN^sLD&WQH]PQHRT_:VuQH]PFH_JD&OHQ=d+ :NPGHObLk\H\*Q~nRTOHILMNP]^JWIm*NPdH]^JWQJ.Nj\*lOH_VkHQH]PNj\~D\*UPNPvG=D5FHItm*RTOHILM5NP]^JW ~oÓD\*UPNPvG=DFHItm*RTOHIMNP]^JΩW ~σΩ×Ø ®ÙPÚÛqÚÜÚÝ^*Þ.ß«H®HàÖ{σ(B)BB[0, 1]f : X −→ Yξ −1 (B)Pξ (B)ξ≡ηξ ár=â ãrâ ηd{{{{{{{{ξ=η{Fξ (x)ξ ár=â ãrâ aξ ∼ PξBi(n, p)P ois(λ)G(p)INRS g dµRS{{{{{{{{g(s) µ(ds){fξ (x)R[a, b]{{N (a, σ 2 )N (0, 1)Φ(x){{{ϕ(x){Φa, σ2 (x){ϕa, σ2 (x){exp(λ)K(a, σ)EξÓo D\*UPNPvG=Dn=FHIGHILM5m*NPOHO=DKyRTOHILM5NP]^JWIR~BvIGHNj\*NPW]PYDK oÓD\*UPNPvG=D~vIGHNj\*NPW]PYDK σ oÓD\*UPNPvG=DFHItm*RTOHIMNP]^JWzI&JGHN^stYD~σ[0, 1]I&JIvG=DMNPOHQHN nm*N^dH]^JW&bf[iNtNSQsW ~fX YFHI\*OH_-dFHGHIIvG=DsERTOHILM5NP]^JW.DFHGHQuI&JIvG=DMNPOHQHQ ~ξG=D&]PFHGHNjm*Nj\*NPOHQ=NX]j\=bk=D&dHOHIdWNj\*BQHkHQHOH_ ~ξJIM5m*N^]^JWNPOHO=INXG=D&WNPOH]^JWI5]j\=bk=D&dHOH_:VWNj\*QHkHQHO Q ~ξ ηG=D&WNPOH]^JWIFHIkJQÀO=D&WNPGHOHIN|PYHWQHW.D\*NPOJOHI]^J.l ]j\=b.ok=D&dHOH_:VuWNj\*QHkHQHO Q ~ξ ηG=D&WNPOH]^JWIÂFHIäG=D&]PFHGHNjm*Nj\*NPOHQHfå]j\=bk=D&dHOH_:VæWNj\*QHkHQHOQ ~ξ ηZbOHYHHQKG=D&]PFHGHNjm*Nj\*NPOHQK]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ ~]j\=bk=D&dHO=DKWNj\*QHkHQHO=D n=W_-GHILM5m*NPOHO=DKuWJIkHYN ξ~]j\=bk=D&dHO=DKWNj\*QHkHQHO=D ξ QHRTNPN^J9G=D&]PFHGHNjm*Nj\*NPOHQ=N a~vQHOHIRTQ=D\*lOHINEG=D&]PFHGHNjξm*Nj\*NPOHQHNS]EF=D&G=D&RTN^JG=D&RTQ Pξ Q ~Fb.D&]P]PIOHIW]PYINXG=D&]PFHGHNjm*Nj\*NPO=QHNS]F=D&G=D&RTN^JGHIR n~ pUPNPIRTN^JGHQHkHNt]PYINSG=D&]PFHGHNjm*Nj\*NPOHQHNS]EF=D&G=D&RTN^JGHIR λ ~pRTOHIMNP]^JWIzO=DJ&bG=D\*lOH_:VukHQH]PNj\~QHOJNPUPG=D\1ÃXNPvNPUjD§ZbOHYHHQHQFHI§RTNPGHNO=DRTOHILMNjogµ]^JWN ~QHOJNPUPSG=D\1ÃXNPvNPUjDZbOHYHHQHQFHI§RTNPGHNO=DRTOHILM5Njogµ]^JWN ~F\*I&JOHSI]^Jl9G=D&]PFHGHNjm*Nj\*NtOHQK]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ ~G=D&WOHIRTNPGHOHIN%G=D&]PFHGHNjm*Nj\*NPOHQHNc]-F=D&G=D&RTN^JG=D&RTQ Q ξ O=Da bI&JGHN^stYN j~OHIGHRaD\*l[a,OHINEb]G=D&]PFHGHNjm*Nj\*NPOHQHNS]EF=D&G=D&RTN^JG=D&RTQ Q 2 ~]^JD&OmD&GJO=INXOHIGHRaD\*lOHINEG=D&]PFHGHNjm*Nj\*NPOHQHN~ a σZbOHYHHQK+G=D&]PFHGHNjm*Nj\*NPOHQK)]^JD&OmD&GJOHIUtI"OHIGHRaD\*lOHIUPIsLD&YIO=D~F\*I&JOHI]^Jl;]^JD&OmD&GJO=IUPI;OHIGHRaD\*l&OHIUPI»G=D&]PFHGHNjm*N\*N^oOHQK~ZbOHYHHQK¸G=D&]PFHGHNjm*Nj\*NPO=QKOHIGHRaD\*lOHIUPI sLD&YIO=D ]F=DoG=D&RTN^JG=D&RTQ Q 2 ~F\*I&JOHI]^JlEOHaIGHRaσD\*lOHIUPIG=D&]PFHGHNjm*Nj\*NPOHQK5]F=D&G=D&RTN^JG=DoRTQ Q 2 ~FHIYaDsLDJσNj\*lOHIN)|PY]PFHIOHNPOHHQ=D\*lOHINL XG=D]PFHGHNjm*Nj\*NtOHQHN"]F=D&G=D&RTN^JGHIR ~G=D&]PFHGHNjm*Nj\*NPOHQ=λNSI&pQu]EF=D&G=D&RTN^JG=D&RTQ Q ~RaDJNPRaDJQHkHNt]PYINSILM9QmD&OHQHNE]j\=bk=D&dHOHI&daWNj\*σQHkHQHOH_ ~σ{{ξ×Ø ®ÙPÚÛ)ÚÜÚÝ^*Þ.ß«H®HàRba{f (x) du(x){IRnDξè L± é (ξ, η){{{ρ(ξ, η)Eξ kE(ξ − Eξ)k{{{E|ξ|k{E|ξ − Eξ|k{Eξ [k]{ϕξ (t){ψξ (z)H ∗GF (s) (x)ξn −→îï ðï ξ{{{P{(r){d{ξn −→ ξξn −→ ξξn −→ ξ{ξn =⇒ ξFn =⇒ F{QHOJNPUPG=D\çJQ\=JlNP]LD`I&J`ZbOHYHHQHQFHI`ZbOHYHHQHQf (x)O=D5IJGHN^stYN~u(x)b]oRTNPGHOHINENPWY\*Qm*[a,IWIzFHGHI]^JG=D&OH]^JWIH~nm*QH]PFHNPGH]PQK]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ ~YIW.D&GHQ=D&HQKy]j\=bk=D&dHOH_:VWNj\*QHkHQHO ξ Q ~ηYI|PZEZEQHHQHNPOJSYIGHGHNj\=KHHQHQ9]j\=bk=D&dHξOH_:VzWNj\*QHkHQHO Q ~ξ ηRTIRTNPOJ9FHI&GKm*YD ]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ ~HNPOJG=D\*lOH_-dRTIRTkNPOJuFHIG.Km*YD]j\=bk=D&dHOHξId WNj\*QHkHQokOH_ ~D&v]PIξ\*f[JOH_-dRTIRTNPOJ§FHIG.Km*YD]j\=bk=D&dHOHIdWNj\*QHkHQokOH_ ~HNPOJξG=D\*lOH_-d;D&v]PI\*f[JOH_d»RTIRTNPOJêFHIGKm*YD]j\=b.okk=D&dHOHIduWNj\*QHkHQHOH_ ~ZXD&YJIGHQ=D\*lOH_-dRTξIRTNPOJzFHIGKm*YD ]j\=bk=D&dHOHIdWNj\*QokkHQHOH_ ~VD&G=D&YJξNPGHQH]^J.QHkHNt]PYDKëZbOHYHHQKì]j\=bk=D&dHOHIdíWNj\*QHkHQoOH_ ~FHGHIξQstWItm=KiDKuZbOHYHHQKu]j\=bk=D&dHOHIdWNj\*QHkHQHOH_ ~ξ]PWNPGJYDzZbOHYHHQHdQ ~H G]PQHRTRTN^JGHQsLD&HQK+ZbOHYHHQHQuG=D&]PFHGHNjm*Nj\*NPO=QK~F (x)]eV.ILm*QHRTI]^Jly]j\=bk=D&dHOH_:VqWNj\*QHkHQHOY)]j\=bk=D&doOHIdWNj\*QHkHQHOHN FHIkJQO=D&WNPGHOHIN]:ξ1W,NPGHξ2IL,K.J.OH.I]^JlfNjm*QoξOHQH=D. j~]eV.ILm*QHRTI]^Jly]j\=bk=D&dHOH_:VqWNj\*QHkHQHOY)]j\=bk=D&doξ 1 , ξ2 , .
Характеристики
Тип файла PDF
PDF-формат наиболее широко используется для просмотра любого типа файлов на любом устройстве. В него можно сохранить документ, таблицы, презентацию, текст, чертежи, вычисления, графики и всё остальное, что можно показать на экране любого устройства. Именно его лучше всего использовать для печати.
Например, если Вам нужно распечатать чертёж из автокада, Вы сохраните чертёж на флешку, но будет ли автокад в пункте печати? А если будет, то нужная версия с нужными библиотеками? Именно для этого и нужен формат PDF - в нём точно будет показано верно вне зависимости от того, в какой программе создали PDF-файл и есть ли нужная программа для его просмотра.
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