Kuhlangana ngekuhamba kwesikhatsi: Umtsetfo wetinombolo letinkhulu ku-roulette
Kutsi silinganiso sitinza njani size sifike ku-−2.70%, nekutsi kungani loko kutsatsa sikhatsi lesidze kunaloko umcondvo lokucabangako.
Kulahlekelwa ngesilinganiso ekujikeleteni ngakunye kusondzela ku-−1/37 njengoba kujikeleta kwandza, kantsi kusabalala kuncipha njenga-1/√N. Ngemuva kwekujikeleta lokungu-1,000 ubheja kulokubovu, silinganiso kanyenti singekhatsi kwa-±3% kwalokulindzelekile.
Umtsetfo wetinombolo letinkhulu
Silinganiso lesichubekako sekubheja lokutimele sitsambekela elinanini lelilindzelekiletibaloLinani lelilindzelekileUmphumela wesilinganiso ngekubheja ngakunye ngekuhamba kwesikhatsi lesidze. −1/37 yelinani lelibhejiwe kuko konkhe kubheja lokujwayelekile kwaseYurophu.Fundza konkhe →. Ngemuva kwekujikeleta lokungu-N kwekubheja lokulingana nemali ngeliyunithiimaliLiyunithiLinani lelibhejwako lelisisekelo luhlelo noma umdlali lasebenta ngalo. Kwenyuswa kwelinani kuchazwa ngemayunithi kute kusebente kunoma ngumuphi litafula.Fundza konkhe → linye, umphumela ngesilinganiso ekujikeleteni ngakunye unelinani lelilindzelekile lelingu-−1/37 kanye nekuphambuka lokujwayelekiletibaloKuphambuka lokujwayelekileImphandze yesikwele yekugucugucuka (variance); libanga lelivamile lemphumela kusuka enanini lelilindzelekile.Fundza konkhe → lokungu-1/√N. Nangabe N = 100 loko kusabalala kungu-10% welinani lelibhejwako, cishe kuphindvwe kane kunesibonakaliso lesingu-2.7%. Nangabe N = 1,000 kungu-3.2%, cishe kuyalingana nesibonakaliso. Nangabe N = 10,000 kungu-1%, futsi inzuzo yelikhasino iyabonakala ngalokucacile. Inzuzo yelikhasino ayibonakali eseshini yinye, kodvwa ayiphikiswa emnyakeni.
Yini letinzako naletingatinzi
Silinganiso ekujikeleteni ngakunye siyatinza. Linani lonkhe alitinzi: liya ngekuya kudze nelicandza njengoba N ikhula, cishe nga-2.7% wa-N ngekwalokulindzelekile, nekusabalala lokungu-√N kuloko. Umdlali lodlale kujikeleta lokungu-10,000 nga-$10 kulindzeleke kutsi abe alahlekelwe ngu-$2,700, kungetwe nobe kususwe $1,000. Silinganiso lesichubekako setinombolo letibovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe → sesinesikhatsi lesidze sitinzile eduze kwa-48.65%; libhalansi lelichubekako alikatinzi ndzawo.
- p10 −$440
- p25 −$280
- phakatsi −$140
- p75 +$0
- p90 +$140
Kungani umcondvo uyakhohlisa
Bantfu balindzele kutsi inzuzo yelikhasino ivele masinyane ngobe 2.70% uvakala amkhulu, futsi balindzele kutsi luchungechunge lolude “lulingane” ngobe umtsetfo wetinombolo letinkhulutibaloUmtsetfo wetinombolo letinkhuluSilinganiso semiphumela letimele sisondzela linani lelilindzelekile njengoba linani lekuzama likhula.Fundza konkhe → utsi tilinganiso tiyatinza. Yomibili lemicondvo iyaphosisa ngebukhulu betintfo: inzuzo yelikhasino incane nangabe icatsaniswa nekugucugucukatibaloKugucugucukaSilinganiso sekutsi imiphumela isabalele kangakanani etungeleta linani lelilindzelekile. Kukhulu ku-straight up, kuncane ekubhejeni lokulingana nemali.Fundza konkhe → kwekujikeleta kunye (σ = liyunithi lelingu-1 nangabe licatsaniswa na-EV = 0.027), ngako kudzinga kujikeleta lokungu-(1/0.027)² ≈ 1,400 kute ibonakale ngesigma sinye. Futsi kutinza kwesilinganiso akwenti lutfo kubuyisela linani lonkhe emuva; kumane kuncishiswe umtselela wekugucugucuka kwangaphambilini.
Kutinza kwalokunye kubheja
Ku-straight upkubhejaI-straight upInombolo yinye, kukhokha 35:1.Fundza konkhe → (kubheja enombolweni yinye) σ = 5.84, ngako sibalo lesifanako sinika kujikeleta lokungu-(5.84/0.027)² ≈ 47,000 kute inzuzo yelikhasino ifike esigmeni sinye. Umdlali we-straight up angadlala iminyaka leminyenti ngaphandle kwekutsi inzuzo yelikhasino ihlukaniseke enhlanhleni emarekhodini akhe, kantsi ukhokha ncamashi 2.70% lofanako nemdlali lobheja kulokubovu loyibona ngekhatsi kwemaviki lambalwa.
Loko lokushiwo ngiloku ekuhloleni tinhlelo
Nobe ngubani lotsi luhlelo luyasebenta kufanele akhone kulukhombisa ngekujikeleta lokungu-10,000 nobe ngetulu nesilinganiso lesihle lesibhaliwe. Ngekujikeleta lokungu-1,000, silinganiso lesihle ekubhejeni lokulingana nemali singavela kanye kulokuhlanu nanoma luhlelo lungenamtselela nekancane (i-null hypothesis); ngekujikeleta lokungu-100 cishe kufana nekuphonsa luhlavu lwemali. Tilingisi kulelisayithi tenta tiseshini letingu-2,000 tebudze lobukhetsile ngemzuzwana munye, lobubufakazi lobunyenti kunanobe ngubani lotsi luhlelo lwamsebentela.
Lifomula
Imibuto
LitfubatibaloLitfubaLitfuba lekutsi umphumela wenteke, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo yinye: 1/37 = 2.70%.Fundza konkhe → lekuphindze ube phambili liyehla liye elicandzeni njengoba udlala. Linani lonkhe liyehla ngaphandle kwemkhawulo.
Cha. Usho kutsi kugucugucuka kwangaphambilini kuba yincenye lencane yesampula lelikhudlwana.
Ekubhejeni lokulingana nemali, cishe lokungu-10,000 ngaphambi kwekutsi inzuzo yelikhasino ibonakale ngalokucacile. Ku-straight up, cishe lokungu-50,000.
Bumnandi betibalo
Zama loku ngekwakho kucala. Sixazululo ngasinye sifihliwe; sivule nawukulungele.
Bangani lababili badlala imijikeleto lengu-20 yemdlalo lolinganakotibaloUmdlalo lolinganakoUmdlalo lapho kute luhlangotsi lolunenzuzo: konkhe kubheja kunelinani lelilindzelekile lelingu-zero.Fundza konkhe →, kuphosa luhlamvu lwemali nobe lokubovukubhejaBovuKubheja lokulingana nemali etinombolweni letingu-18 letibovu. NgesiFulentji: rouge.Fundza konkhe → kumelana nalokumnyamakubhejaMnyamaKubheja lokulingana nemali etinombolweni letingu-18 letimnyama. NgesiFulentji: noir.Fundza konkhe → lapho emacandzalisondvoLicandzaUmgodzi munye loluhlata longambonjwa kubheja lokulingana nemali, kwelidazini noma kwelikholamu; umtfombo wenzuzo yelikhasino. Kuphindze kutsiwe: licandza linye, 0.Fundza konkhe → abuyiselwa khona, futsi bagcina emaphuzu lachubekako. Bala imijikeleto lapho ngamunye asembili kuyo (kulingana kubalelwa loyo lobekasembili ngaphambi nje kwaloko). Yini lenelitfuba lelikhulu: kutsi kuba sembili kwabelwana ngemijikeleto lengu-10 ku-10, nobe kutsi umngani munye ahole yonkhe lengu-20?
Khombisa sixazululo
Imphendvulo Umngani munye lohola yonkhe imijikeleto lengu-20 unelitfuba lelikhulu kakhulu: 35.2%, nobe nguwuphi umngani, ngekucatsaniswa na-6.1% wekwabelana lokulinganako kwa-10 ku-10.
Litfuba lekutsi emaphuzu lachubekako emdlalweni lolinganako alingane ngemuva kwemijikeleto lengu-2k ngu-u = C(2k, k)/2²ᵏ: 0.246 ngemuva kwemijikeleto lengu-10 na-0.176 ngemuva kwalengu-20. Umphumela lowatiwako, umtsetfo we-arc-sine, utsi litfuba lekutsi umngani lobitwe ngeligama ahole ncamashi imijikeleto lengu-2k kulengu-2n ngu-u(2k) × u(2n − 2k).
Kuhola yonkhe lengu-20: u(20) × u(0) = 0.176 kumngani ngamunye, 35.2% kunobe nguwuphi. Kwabelana lokulinganako: u(10) × u(10) = 0.246² = 6.1%, kwabelana lokunelitfuba lelincane kakhulu kunako konkhe.
Ngako emdlalweni lolinganako kuhola akuvamisi kushintja tandla. Umdlali lobekasembili kuyo yonkhe lemini, nobe semuva kuyo yonkhe lemini, akabonanga lutfo lolungajwayelekile, futsi loko akusho lutfo ngelisondvo nobe ngelikhono. Epstein (2013) unika umtsetfo lofanako wemidlalo lemidze: ingcenye yesikhatsi luhlangotsi lolunenhlanhla kakhulu luhola ngetulu kwa-85% wemdlalo.
Lokuhlekisako
Silinganiso siyatinza. Linani lonkhe limane lihambe.
Imitfombo
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.