Ɓadagol e Juuta: Sariya Limooje Mawɗe e Ruleet
Hono hakkundeere nden tabitorta e −2,70%, e ko waɗi ɗum ina juuta ko ɓuri ko neɗɗo sikki.
Majjere hakkundeere e taarol kala ina ɓadoo −1/37 nde taarle ɓeydotoo, yaajeende mum ina ustoo hono 1/√N. Caggal taarle 1 000 e boɗeere, hakkundeere ndee ko ko heewi ina woni nder ±3% fodaande mum.
Sariya limooje mawɗe
Hakkundeere jokkondirnde pariiji ceertuɗi ina ɓadoo njaru fodaandumatematikNjaru fodaanduNjeñtudi hakkundeere e kala pari e juuta. −1/37 pari ngam kala pari Orop laawol.Tar fof → ndee. Caggal taarle N e pari njoɓdi fotndi e initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → wootere, njeñtudi hakkundeere e taarol kala ina jogii fodaande −1/37 e seerndu ndenndaandumatematikSeerndu ndenndaanduRaasin karee wariyaas; ko woɗɗeende aadanteende njeñtudi e njaru fodaandu.Tar fof → 1/√N. E N = 100, yaajeende ndee ko 10% pari, ɓadii laabi nay maande 2,7% ndee. E N = 1 000 ko 3,2%, ina fota hedde e maande ndee. E N = 10 000 ko 1%, ɓural ngal ina yiyoo laaɓtude. Ɓural ngal yiyataake nder jonnde wootere, kono ina laaɓi nder hitaande.
Ko ɓadotoo e ko ɓadotaako
Hakkundeere e taarol kala ina ɓadoo. Kawtal ngal ɓadotaako: ina woɗɗitoo seero nde N ɓeydotoo, hono 2,7% N e fodaande, e yaajeende √N e takko ɗum. Fijoowo fijii taarle 10 000 e $10 ina fodaa majjude $2 700, ɓeydi walla ustii $1 000. Feccere limooje boɗeejepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → ndee tabitii ko booyi e takko 48,65%; kaalis heddiiɗo oo tabitaaki fey.
- p10 −$440
- p25 −$280
- medyan −$140
- p75 +$0
- p90 +$140
Ko waɗi miijo neɗɗo ina juumi
Yimɓe ina sikki ɓural ngal ina yiyoo law sabu 2,70% ina wayi no ko heewi, ina sikki kadi jokkondire juutɗe ina “fotndoo” sabu sariya limooje mawɗematematikSariya limooje mawɗeHakkundeere njeñtuɗi ceertuɗi ina ɓadoo njaru fodaandu tuma nde limoore etaaɗe ɓeydotoo.Tar fof → ina wiya hakkundeeje ina ɓadoo. Miijooji ɗiɗi ɗii fof ina juumi e mawneede: ɓural ngal ko tokooso so fondaa e wariyaasmatematikWariyaasPeeta no njeñtuɗi saŋkitiri e njaru fodaandu. Ina toowi ngam limoore wootere, ina lesɗi ngam pariiji njoɓdi fotndi.Tar fof → taarol gooto (σ = 1 inite e EV = 0,027), ɗum noon ina naami (1/0,027)² ≈ 1 400 taarle ngam ɗum yiyee e sigma gooto. Kadi ɓadagol hakkundeere ndee ruttataa kawtal ngal e caggal; ina tokoosina tan ɓeydagol e ustagol ɓennuɗi.
Ɓadagol e pariiji goɗɗi
E pariiji limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → σ = 5,84, ndeen hiisa gooto oo ina rokka (5,84/0,027)² ≈ 47 000 taarle ngam ɓural ngal yettinde sigma gooto. Fijoowo limoore wootere ina waawi fijaade duuɓi tawa ɓural ngal seertinaaki e sahaa nder binndi mum, ko o yoɓata 2,70% gooto oo tigi hono fijoowo boɗeere yiyoowo ɗum nder yontereeji seeɗa.
Ko ɗum firti e ƴeewgol sistemji
Kala wiyoowo sistem ina gollira, ina foti hollirde ɗum e taarle 10 000 walla ko ɓuri, e hakkundeere ɓurnde seero winndaande. E taarle 1 000, hakkundeere ɓurnde seero e njoɓdi fotndi ko huunde waɗotoonde laabi gooto e nder joy so tawii sistem ngal alaa nafoore; e taarle 100 ina ɓadii hono weddugol kaalis (yeeso walla caggal). Simulateerji lowre ndee ina ndogna jonɗe 2 000 juutal ngal suɓaa-ɗaa nder segonde wootere, ɗum ko seede ɓurnde seedeeji yimɓe fof.
Formil
Naamne
PorobabilitematematikPorobabiliteSahaa njeñtudi, immorde 0 haa 1 walla 0% haa 100%. Limoore wootere: 1/37 = 2,70%.Tar fof → ruttaade e dañal kadi ina ustoo haa ɓadoo seero nde fijotoɗaa. Kawtal ngal ina jippoo tawa alaa keerol.
Alaa. Ina firti ɓeydagol e ustagol ɓennuɗi ina ngonta feccere ɓurnde tokoosude e misal ɓurngal mawnude.
E njoɓdi fotndi, hono 10 000 ado ɓural ngal yiyee laaɓtude. E limoore wootere, hono 50 000.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
Sehilaaɓe ɗiɗo ina pija taarle 20 fijo potngomatematikFijo potngoFijo ngo hay sera wootere alaa ɓural: kala pari ina jogii njaru fodaandu potndu e seero.Tar fof →, werlugol kaalis walla boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → e yeeso ɓaleerepariƁaleerePari njoɓdi fotndi e limooje 18 ɓaleeje. E Farayse: noir.Tar fof → tawa seerotaarordeSeeroSuudu haako wootere nde hay pari njoɓdi fotndi, sappo e ɗiɗi walla kolon kuuɓataa; ko ɗum woni iwdi ɓural kasino. Ina noddee kadi: seero gooto, 0.Tar fof → ina ruttee, ina njokkita limoore maɓɓe. Limtu taarle ɗe kala e maɓɓe woni yeeso (fotde ina limtee ngam on mo woni yeeso hade ɗum). Hol ko ɓuri waawde waɗude: yeeso ngoo senndaa taarle 10 e 10, walla sehil gooto ina woni yeeso taarle 20 ɗee fof?
Hollu jaabawol ngol
Jaabawol Sehil gooto wonde yeeso taarle 20 ɗee fof ɓuri waawde waɗude no feewi: 35,2%, so kala e maɓɓe ina limtee, e yeeso 6,1% ngam senndugol potngol 10 e 10.
Porobabilite nde limoore potnde jokkitaande fotata caggal taarle 2k ko u = C(2k, k)/2²ᵏ: 0,246 caggal taarle 10 e 0,176 caggal 20. Njeñtudi ganndaandi, sariya arcsinus, ina wiya porobabilite nde sehil innaaɗo wonata yeeso taarle 2k tigi e nder 2n ko u(2k) × u(2n − 2k).
Wonde yeeso taarle 20 ɗee fof: u(20) × u(0) = 0,176 ngam kala sehil, 35,2% ngam kala e maɓɓe. Senndugol potngol: u(10) × u(10) = 0,246² = 6,1%, senndugol ɓurngol famɗude porobabilite fof.
Ɗum waɗi e fijo potngo, yeeso ngoo waylotaake juuɗe sahaa heewɗo. Fijoowo woniino yeeso kiikiiɗe ndee fof, walla caggal kiikiiɗe ndee fof, yi'aani hay huunde ko wonaa aadanteeɗo, ɗum wiyataa hay huunde e taarorde ndee walla e ganndal. Epstein (2013) ina rokka sariya gootal ngal ngam fijooji ɓurɗi juutde: feccere sahaa, gedal ɓurngal hawrude ina woni yeeso ko ɓuri 85% fijo ngoo.
Ƴeewndo weltinoowo
Hakkundeere ina ɓadoo. Kawtal ngal ko yahude tan.
Iwdi
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.