Ukusondela ngokuhamba kwexesha: umthetho wamanani amakhulu kwi-roulette
Indlela umndilili ozinza ngayo usiya ku-−2.70%, nesizathu sokuba oko kuthathe ixesha elide kunokuba ingqondo icinga.
Ilahleko yomndilili ngomjikelo isondela ku-−1/37 njengoko imijikelo isanda, kunye nosasazo olunciphayo njenge-1/√N. Emva kwemijikelo eli-1,000 kobomvu umndilili uhlala ungaphakathi kwe-±3% kokulindelekileyo kuwo.
Umthetho wamanani amakhulu
Umndilili oqhubekayo weebheji ezizimeleyo usondela kwixabiso elilindelekileyoizibaloIxabiso elilindelekileyoIsiphumo esiphakathi kwibheji nganye ekuhambeni kwexesha elide. −1/37 yebheji kuyo yonke ibheji eqhelekileyo yaseYurophu.Funda yonke →. Emva kwemijikelo engu-N yemali elinganayo nge-yunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → enye, isiphumo somndilili ngomjikelo sinokulindelekileyo okungu-−1/37 kunye nokutenxa okuqhelekileyoizibaloUkutenxa okuqhelekileyo (standard deviation)Ingcambu yesikwere yokwahluka; umgama oqhelekileyo wesiphumo ukusuka kwixabiso elilindelekileyo.Funda yonke → okungu-1/√N. Ku-N = 100 olo sasazo yi-10% yebheji, phantse amaxesha amane omqondiso we-2.7%. Ku-N = 1,000 yi-3.2%, malunga nokufana nomqondiso. Ku-N = 10,000 yi-1%, kwaye inzuzo yekhasino ibonakala ngokucacileyo. Inzuzo yekhasino ayibonakali kwiseshoni kodwa ayinakuphoswa kunyaka.
Yintoni esondelayo nengasondeliyo
Umndilili ngomjikelo uyasondela. Iyonke ayisondeli: ihamba kude neqanda njengoko u-N ekhula, malunga ne-2.7% ka-N ngokulindelekileyo, kunye nosasazo lwe-√N malunga naloo nto. Umdlali odlale imijikelo eli-10,000 nge-$10 kulindeleke ukuba asilele nge-$2,700, ngaphezulu okanye ngaphantsi kwe-$1,000. Umlinganiselo oqhubekayo wobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → kudala wazinza kufuphi ne-48.65%; ibhalansi eqhubekayo ayikazinzi naphi na.
- p10 −$440
- p25 −$280
- umbindi −$140
- p75 +$0
- p90 +$140
Kutheni ingqondo isilela
Abantu balindele ukuba inzuzo yekhasino ibonakale ngokukhawuleza kuba i-2.70% ivakala ininzi, kwaye balindele ukuba uthotho olude “lulingane” kuba umthetho wamanani amakhuluizibaloUmthetho wamanani amakhuluUmndilili weziphumo ezizimeleyo usondela kwixabiso elilindelekileyo njengoko inani lemizamo likhula.Funda yonke → uthi imindilili iyasondela. Zombini ezi ngcinga ziyiqikelela kakubi isikali: inzuzo yekhasino incinci xa ithelekiswa nokwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke → komjikelo omnye (σ = iyunithi e-1 ngokuchasene ne-EV = 0.027), ngoko kuthatha (1/0.027)² ≈ imijikelo eli-1,400 ukuze ibonakale nge-sigma enye. Kwaye ukusondela komndilili akwenzi nto ukubuyisa iyonke; kuxuba nje ukujingajinga okudlulileyo.
Ukusondela kwezinye iibheji
Kwi-bheji yenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke → σ = 5.84, ngoko ubalo olufanayo lunika (5.84/0.027)² ≈ imijikelo engama-47,000 ukuze inzuzo yekhasino ifikelele kwi-sigma enye. Umdlali webheji yenani elinye angadlala iminyaka ngaphandle kokuba inzuzo yekhasino yahlulwe kwithamsanqa kwiirekhodi zakhe, ngelixa ehlawula kanye i-2.70% efanayo nomdlali wobomvu oyibona kwiiveki ezimbalwa.
Okuthethwa koku ekuvavanyeni iinkqubo
Nabani na othi inkqubo iyasebenza kufuneka akwazi ukuyibonisa kwimijikelo eli-10,000 nangaphezulu enomndilili olungileyo obhaliweyo. Kwimijikelo eli-1,000 umndilili olungileyo kwimali elinganayo sisiganeko esinye kwezintlanu phantsi kwe-null; kwimijikelo eli-100 phantse kukuphosa ingqekembe. Izilinganisi ezikule sayithi ziqhuba iiseshoni ezingama-2,000 zobude obukhethileyo ngomzuzwana, obubungqina obungaphezulu kobuphi na ubungqina bomntu.
Ifomula
Imibuzo
AmathubaizibaloAmathubaIthuba lesiphumo, ukusuka ku-0 ukuya ku-1 okanye ku-0% ukuya ku-100%. Inani elinye: 1/37 = 2.70%.Funda yonke → okuphinda ube phambili ayehla esiya kwiqanda njengoko udlala. Iyonke ihla ngaphandle komda.
Hayi. Uthetha ukuba ukujingajinga okudlulileyo kuba yinxalenye encinci yesampuli enkulu.
Kwimali elinganayo, malunga ne-10,000 ngaphambi kokuba inzuzo yekhasino ibonakale ngokucacileyo. Kwiibheji zenani elinye, malunga nama-50,000.
Ukonwaba ngezibalo
Qala uzizame ngokwakho. Isisombululo ngasinye sisongiwe; sivule xa ukulungele.
Abahlobo ababini badlala imijikelo engama-20 yomdlalo ofanelekileyoizibaloUmdlalo onobulungisaUmdlalo apho kungekho cala linenzuzo: yonke ibheji inexabiso elilindelekileyo eliliqanda.Funda yonke →, ukuphosa ingqekembe okanye obomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → ngokuchasene nomnyamaibhejiOmnyamaIbheji yemali elinganayo kumanani ali-18 amnyama. NgesiFrentshi: noir.Funda yonke → kunye namaqandaiviliIqandaIsikhewu esinye esiluhlaza esingagubungelwa yibheji yemali elinganayo, yedazini okanye yekholamu; umthombo wenzuzo yekhasino. Kwakhona: iqanda elinye, 0.Funda yonke → abuyiswayo, kwaye bagcina amanqaku aqhubekayo. Bala imijikelo apho ngamnye wabo ephambili (ukulingana kubalelwa lowo ubephambili kanye ngaphambili). Yintoni enokwenzeka ngakumbi: ukuba ukuba phambili kwabelwana ngemijikelo eli-10 kwengeli-10, okanye ukuba umhlobo omnye uphambili kuyo yonke engama-20?
Bonisa isisombululo
Impendulo Umhlobo omnye ephambili kuyo yonke imijikelo engama-20 kunokwenzeka kakhulu: 35.2%, kubalwa nawuphi na umhlobo, xa kuthelekiswa ne-6.1% yokwabelana ngokulinganayo kwe-10 ku-10.
Ithuba lokuba amanqaku aqhubekayo omdlalo ofanelekileyo alingane emva kwemijikelo engama-2k ngu-u = C(2k, k)/2²ᵏ: 0.246 emva kwemijikelo eli-10 kunye no-0.176 emva kwengama-20. Isiphumo esidumileyo, umthetho we-arc-sine, uthi ithuba lokuba umhlobo omnye ochaziweyo abe phambili kwimijikelo engama-2k ngqo kwengama-2n ngu-u(2k) × u(2n − 2k).
Ukuba phambili kuyo yonke engama-20: u(20) × u(0) = 0.176 kumhlobo ngamnye, 35.2% kunawuphi na. Ukwabelana ngokulinganayo: u(10) × u(10) = 0.246² = 6.1%, esona sabelo singenakwenzeka kunazo zonke.
Ngoko kumdlalo ofanelekileyo ukuba phambili akufane kutshintshe izandla. Umdlali obephambili ubusuku bonke, okanye esemva ubusuku bonke, akabonanga nto ingaqhelekanga, kwaye oko akuthethi nto ngevili okanye ngobuchule. U-Epstein (2013) unika umthetho ofanayo wemidlalo emide: isiqingatha sexesha icala elinethamsanqa ngakumbi liphambili ngaphezu kwe-85% yomdlalo.
Uncumo
Umndilili uyasondela. Iyonke iyahamba nje.
Imithombo
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.