TEOREMAHOI HUDUDIi nazariyai ehtimoliyat

TEOREMAHOI HUDUDIi nazariyai ehtimoliyat, yakchand teoremahoi nazariyai ehtimoliyatro nomand, ki sharthoi ba vujud omadani in yo on qonuniyathoro sobit mekunand (dar natijai tasiri miqdori kaloni omilhoi tasodufi).

Teoremai Bernulli (1713) va teoremai Laplas (1812) nakhustin teoremahoi hududi meboshand, ki vobastagii taqsimoti tamoyuli basomadi nisbii ruy dodani yagon hodisai E (dar n ozmoishi novobasta) va ehtimoliyati ruy dodani hodisa r (0<r<1)-ro sobit mekunand. Nisbati m/n basomad nom dorad, ki in jo m miqdori ruy dodani hodisai E dar n ozmoish ast.

Soli 1837 in teoremahoro S. Puasson hangomi az k vobasta budani ehtimoliyati () dar ozmoishi k-um ruy dodani hodisai E tatbiq namud va dar mavridi  vobastagii hududii taqsimoti tamoyuli basomadi m/n va qimati miyonai arifmetikii (r) ehtimoliyati  ()-ro nishon dod:

Agar  buzurgii tasodufie boshad, ki hangomi dar k ozmoish ruy dodani hodisai E qimatash ba yak yo hangomi ruy nadodani hodisa on ba sifr barobar shavad, on goh m -ro dar shakli

navishtan mumkin ast. In ifoda baroi muoinai teoremahoi mazkur hamchun holati khususii teoremahoi hududii umumii mansubi summai buzurgihoi tasodufii novobasta (qonuni adadhoi kalon va teoremai hududii markazi) imkon medihad. Sharthoi musoidi tatbiqpazirii qonuni adadhoi kalonro P. L. Chebishev (soli 1867) kashf kard. Bad in sharthoro A. A. Markov tamimi matematiki dod. A. N. Kolmogorov (masalai sharthoi zaruri va kofii tatbiqpazirii qonuni adadhoi kalonro purra hal namud. A. Ya. Khinchin nishon dod ki hangomi sohibi hamon yak funksiyai taqsimot budani buzurgihoi  in shartho ifodai zaylro sobit mekunand: buaurgihoi  boyad intizoriyati matematikii okhirnok doshta boshand.

Qonuni adadhoi kalon. Biguzor (*) paydarapaii buzurgihoi tasodufii novobasta, — summai n elemengti avvali in paydarpai

va  muvofiqan intizoriyati matematiki

va dispersiyai  summai  boshand. Agar baroi har guna  ehtimoliyati nobarobarii  hangomi  ba sifr mayl kunad, paydarpaii (*)ba qonuni adadhoi kalon muvofiqat mekunad.

Teoremai hududii markazi. Agar baroi harguna , va  ehtimoliyati nobarobarii

dar holati  doroi hududi

boshad, teoremai hududii markazi dar paydarpaii (*) tatbiqpazir ast.

Sharthoi nisbatan umumi va kofii tatbiqpazirii teoremai hududii markaziro Chebishev nishon dod (1887), ammo kambudihoi isboti uro Markov badtar purra namud (1807). Halli masalaero, ki ba halli okhirin monand bud, A. M. Lyapunov yoft (1901). Tarifi daqiqi teoremai Lyapunov chunin ast. Biguzor

va  boshad. Agar nnsbati  hangomi  ba sifr mayl kunad, on goh ba ifodai (*) teoremai hududii markazi tatbiqpazir ast. S. N. Bernshteyn masalai sharthoi tatbiqpazirii teoremai hududii markaziro dar shaklhoi umumi yoft (1926) va F. Feller onro purra namud (1935).

M. Muminov.