Ukuhlangana ngokuhamba kwesikhathi: Umthetho wezinombolo ezinkulu ku-roulette
Ukuthi isilinganiso sizinza kanjani size sifike ku-−2.70%, nokuthi kungani lokho kuthatha isikhathi eside kunalokho umqondo okucabangayo.
Ukulahlekelwa okumaphakathi ngokujikeleza ngakunye kusondela ku-−1/37 njengoba ukujikeleza kwanda, kanti ukusabalala kuncipha njengo-1/√N. Ngemuva kokujikeleza okungu-1,000 ubheja kumbala obomvu, isilinganiso ngokuvamile singaphakathi kuka-±3% kwenani elilindelekile.
Umthetho wezinombolo ezinkulu
Isilinganiso esiqhubekayo sokubheja okuzimele sithambekela enanini elilindelekileizibaloInani elilindelekileUmphumela ovamile ekubhejeni ngakunye esikhathini eside. U-−1/37 wenani elibhejwayo kukho konke ukubheja okujwayelekile kwaseYurophu.Funda konke →. Ngemuva kokujikeleza okungu-N kokubheja okulingana nemali ngeyunithiimaliIyunithiInani elibhejwayo eliyisisekelo uhlelo noma umdlali asebenza ngalo. Ukwenyuswa kwenani kuchazwa ngamayunithi ukuze kusebenze kunoma yiliphi itafula.Funda konke → elilodwa, umphumela omaphakathi ngokujikeleza ngakunye unenani elilindelekile elingu-−1/37 kanye nokuchezuka okujwayelekileizibaloUkuchezuka okujwayelekileImpande yesikwele yokuguquguquka (variance); ibanga elivamile lomphumela ukusuka enanini elilindelekile.Funda konke → okungu-1/√N. Uma u-N = 100 lokho kusabalala kungu-10% wenani elibhejwayo, cishe kuphindwe kane kunophawu olungu-2.7%. Uma u-N = 1,000 kungu-3.2%, cishe kuyalingana nophawu. Uma u-N = 10,000 kungu-1%, futhi inzuzo yekhasino ibonakala ngokucacile. Inzuzo yekhasino ayibonakali eseshinini eyodwa, kodwa ayinakuphikwa onyakeni.
Yini ezinzayo nengazinzi
Isilinganiso ngokujikeleza ngakunye siyazinza. Isamba asizinzi: siya ngokuya kude neqanda njengoba u-N ekhula, cishe ngo-2.7% ka-N ngokwenani elilindelekile, nokusabalala okungu-√N kuzungeze lokho. Umdlali odlale ukujikeleza okungu-10,000 ngo-$10 kulindeleke ukuthi abe elahlekelwe ngu-$2,700, kungeze noma kususwe u-$1,000. Isilinganiso esiqhubekayo sezinombolo ezibomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → sekunesikhathi eside sizinze eduze kuka-48.65%; ibhalansi eqhubekayo ayikazinzi ndawo.
- p10 −$440
- p25 −$280
- phakathi −$140
- p75 +$0
- p90 +$140
Kungani umqondo ukhohlisa
Abantu balindele ukuthi inzuzo yekhasino ivele ngokushesha ngoba u-2.70% uzwakala emkhulu, futhi balindele ukuthi uchungechunge olude “lulingane” ngoba umthetho wezinombolo ezinkuluizibaloUmthetho wezinombolo ezinkuluIsilinganiso semiphumela ezimele sisondela enanini elilindelekile njengoba inani lemizamo likhula.Funda konke → uthi izilinganiso ziyazinza. Yomibili le mibono iyaphosisa ngobukhulu bezinto: inzuzo yekhasino incane uma iqhathaniswa nokuguquguqukaizibaloUkuguquguqukaIsilinganiso sokuthi imiphumela ihlakazeke kangakanani ezungeze inani elilindelekile. Kuphezulu ku-straight up, kuphansi ekubhejeni okulingana nemali.Funda konke → kokujikeleza okukodwa (σ = iyunithi elingu-1 uma kuqhathaniswa no-EV = 0.027), ngakho kudinga ukujikeleza okungu-(1/0.027)² ≈ 1,400 ukuze ibonakale ngesigma esisodwa. Futhi ukuzinza kwesilinganiso akwenzi lutho ukubuyisela isamba emuva; kumane kunciphise umthelela wokuguquguquka kwangaphambili.
Ukuzinza kokunye ukubheja
Ku-straight upukubhejaI-straight upInombolo eyodwa, kukhokha u-35:1.Funda konke → (ukubheja enombolweni eyodwa) u-σ = 5.84, ngakho isibalo esifanayo sinikeza ukujikeleza okungu-(5.84/0.027)² ≈ 47,000 ukuze inzuzo yekhasino ifike esigmeni esisodwa. Umdlali we-straight up angadlala iminyaka eminingi ngaphandle kokuthi inzuzo yekhasino ihlukaniseke nenhlanhla emarekhodini akhe, kanti ukhokha u-2.70% ofanayo ncamashi nomdlali obheja kumbala obomvu oyibona ngaphakathi kwamasonto ambalwa.
Okushiwo yilokhu ekuhloleni izinhlelo
Noma ubani othi uhlelo luyasebenza kufanele akwazi ukulubonisa ngokujikeleza okungu-10,000 noma ngaphezulu nesilinganiso esihle esibhaliwe. Ngokujikeleza okungu-1,000, isilinganiso esihle ekubhejeni okulingana nemali singavela kanye kokuhlanu ngisho noma uhlelo lungenamthelela nhlobo (i-null hypothesis); ngokujikeleza okungu-100 cishe kufana nokuphonsa uhlamvu lwemali. Izilingisi kule sayithi zenza amaseshini angu-2,000 obude obukhethile ngomzuzwana owodwa, okuwubufakazi obuningi kunanoma yimuphi umuntu othi uhlelo lwamsebenzela.
Ifomula
Imibuzo
AmathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → okuphinde ube phambili ayehla aye eqandeni njengoba udlala. Isamba sehla ngaphandle komkhawulo.
Cha. Usho ukuthi ukuguquguquka kwangaphambili kuba yingxenye encane yesampula elikhudlwana.
Ekubhejeni okulingana nemali, cishe okungu-10,000 ngaphambi kokuthi inzuzo yekhasino ibonakale ngokucacile. Ku-straight up, cishe okungu-50,000.
Ubumnandi bezibalo
Zama lezi ngokwakho kuqala. Isixazululo ngasinye sifihliwe; sivule uma usukulungile.
Abangane ababili badlala imizuliswano engu-20 yomdlalo olungileizibaloUmdlalo olinganayoUmdlalo lapho kungekho hlangothi olunenzuzo: konke ukubheja kunenani elilindelekile eliyiqanda.Funda konke →, ukuphonsa uhlamvu lwemali noma bomvuukubhejaBomvuUkubheja okulingana nemali ezinombolweni eziyi-18 ezibomvu. NgesiFulentshi: rouge.Funda konke → ngokumelene no-mnyamaukubhejaMnyamaUkubheja okulingana nemali ezinombolweni ezimnyama eziyi-18. NgesiFulentshi: noir.Funda konke → lapho amaqandaisondoIqandaIgodi elilodwa eliluhlaza elingambozwa ukubheja okulingana nemali, okwedazini noma okwekholamu; umthombo wenzuzo yekhasino. Kubuye kuthiwe: iqanda elilodwa, 0.Funda konke → ebuyiselwa khona, futhi bagcina amaphuzu aqhubekayo. Bala imizuliswano lapho ngamunye ehamba phambili (ukulingana kubalelwa lowo obehamba phambili ngaphambi nje kwalokho). Yikuphi okunamathuba amakhulu: ukuthi ukuhola kwabelwana ngemizuliswano engu-10 ku-10, noma ukuthi umngane oyedwa uhola yonke engu-20?
Bonisa isixazululo
Impendulo Umngane oyedwa ohola yonke imizuliswano engu-20 unamathuba amakhulu kakhulu: 35.2%, kubalwa noma yimuphi umngane, uma kuqhathaniswa no-6.1% wokulingana okungu-10 ku-10.
Amathuba okuthi amaphuzu aqhubekayo omdlalo olungile alingane ngemuva kwemizuliswano engu-2k angu-u = C(2k, k)/2²ᵏ: 0.246 ngemuva kwemizuliswano engu-10 no-0.176 ngemuva kwengu-20. Umphumela odumile, umthetho we-arc-sine, uthi amathuba okuthi umngane oqanjiwe ahole imizuliswano engu-2k ncamashi kwengu-2n angu-u(2k) × u(2n − 2k).
Ukuhola yonke engu-20: u(20) × u(0) = 0.176 kumngane ngamunye, 35.2% kunoma yimuphi. Ukwabelana ngokulinganayo: u(10) × u(10) = 0.246² = 6.1%, ukwabelana okunamathuba amancane kunakho konke.
Ngakho emdlalweni olungile akuvamile ukuthi ukuhola kudlulele komunye. Umdlali obehamba phambili ubusuku bonke, noma osemuva ubusuku bonke, akabonanga lutho olungajwayelekile, futhi lokho akusho lutho ngesondo noma ngekhono. U-Epstein (2013) unikeza umthetho ofanayo wemidlalo emide: ingxenye yesikhathi uhlangothi olunenhlanhla kakhulu luhola ngaphezu kuka-85% womdlalo.
Okokuhlekisa
Isilinganiso siyazinza. Isamba simane sihambe.
Imithombo
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.