Isku-soo-dhowaanshaha Muddada Dheer: Sharciga Tirooyinka Waaweyn ee Roulette
Sida celceliska u dego xagga −2.70%, iyo sababta ay taasi u qaadato waqti ka badan inta dareenku filayo.
Celceliska khasaaraha wareeggii wuxuu u soo dhowaadaa −1/37 marka wareegyadu bataan, isagoo kala-fidsanaantiisu u yaraanayso sida 1/√N. Kadib 1,000 wareeg oo casaan ah, celcelisku inta badan wuxuu ku jiraa ±3% qiimihiisa la filayo.
Sharciga tirooyinka waaweyn
Celceliska socda ee sharadyada madaxbannaan wuxuu u janjeeraa qiimaha la filayoxisaabQiimaha la filayoCelceliska natiijada sharad kasta muddada dheer. −1/37 ee sharadka sharad kasta oo Yurub caadi ah.Akhri dhammaan →. Kadib N wareeg oo lacag isle'eg ah oo hal unuglacagUnugSharadka saldhigga ah ee nidaam ama ciyaartoy ku shaqeeyo. Kordhinnada waxaa lagu sharxaa unugyo si ay ugu shaqeeyaan miis kasta.Akhri dhammaan → ah, natiijada celceliska ah ee wareeggii waxay leedahay qiime la filayo −1/37 iyo leexasho caadi ahxisaabLeexashada caadiga ahXididka labajibbaarka ee kala-duwanaanshaha; masaafada caadiga ah ee natiijo ay u jirto qiimaha la filayo.Akhri dhammaan → 1/√N. Marka N = 100, kala-fidsanaantaasi waa 10% sharadka, ku dhawaad afar jeer calaamadda 2.7%. Marka N = 1,000 waa 3.2%, qiyaastii la mid ah calaamadda. Marka N = 10,000 waa 1%, faa'iidada kasiinaduna si cad ayay u muuqataa. Faa'iidada kasiinadu fadhi gudihiisa ma muuqato, sannad gudihiisana lama dafiri karo.
Waxa isu soo dhowaada iyo waxa aan isu soo dhowaan
Celceliska wareeggii wuu isu soo dhowaadaa. Wadartu ma soo dhowaato: way ka sii fogaataa eber marka N koraayo, qiyaastii 2.7% N si la filayo, iyadoo kala-fidsanaan √N ah ay ku wareegsan tahay. Ciyaartoy ciyaaray 10,000 wareeg oo $10 ah waxaa laga filayaa inuu ku jiro khasaare $2,700, kor ama hoos $1,000. Saamiga socda ee casaankasharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → wuxuu muddo dheer ku degay meel u dhow 48.65%; haraaga socda meelna kuma degin.
- p10 −$440
- p25 −$280
- dhexdhexaad −$140
- p75 +$0
- p90 +$140
Sababta dareenku u khaldamo
Dadku waxay filayaan in faa'iidada kasiinadu si dhakhso ah u muuqato sababtoo ah 2.70% waxay u egtahay wax badan, waxayna filayaan in taxanayaasha dhaadheer ay “is-dheelli tiraan” sababtoo ah sharciga tirooyinka waaweynxisaabSharciga tirooyinka waaweynCelceliska natiijooyinka madaxbannaan wuxuu u soo dhowaadaa qiimaha la filayo marka tirada tijaabooyinku korodho.Akhri dhammaan → wuxuu leeyahay celcelisyadu way isu soo dhowaadaan. Labada dareenba waxay si khaldan u qiimeeyaan baaxadda: faa'iidada kasiinadu way yar tahay marka loo eego kala-duwanaanshahaxisaabKala-duwanaanshoCabbir muujinaya sida ballaaran ee natiijooyinku ugu kala firdhsan yihiin qiimaha la filayo agtiisa. Sare hal lambar, hoose sharadyada lacag isle'eg.Akhri dhammaan → hal wareeg (σ = 1 unug marka la barbar dhigo EV = 0.027), sidaas darteed waxay qaadataa (1/0.027)² ≈ 1,400 wareeg si ay u muuqato heer hal-sigma ah. Isku-soo-dhowaanshaha celcelisku waxba kama qabto inuu wadarta dib u soo jiido; wuxuu kaliya dhex-milaa isbeddelladii hore.
Isku-soo-dhowaanshaha sharadyada kale
Sharadyada hal lambarsharadHal lambarHal lambar oo keliya, wuxuu bixiyaa 35:1.Akhri dhammaan → σ = 5.84, sidaas darteed isla xisaabtu waxay bixisaa (5.84/0.027)² ≈ 47,000 wareeg si faa'iidada kasiinadu u gaarto hal sigma. Ciyaartoy hal lambar ku sharadsada wuxuu ciyaari karaa sannado iyadoo faa'iidada kasiinada aan laga kala saari karin nasiib diiwaannadiisa gaarka ah, isagoo bixinaya isla 2.70% sida ciyaartoyga casaanka ee arka toddobaadyo gudahood.
Waxa ay ka dhigan tahay tijaabinta nidaamyada
Qof kasta oo sheegta in nidaam shaqeeyo waa inuu awoodaa inuu ku muujiyo 10,000 wareeg ama ka badan oo leh celcelis togan oo diiwaangashan. Marka 1,000 wareeg, celcelis togan oo lacag isle'eg ah waa dhacdo shan meelood meel ah iyadoo male-awaalka eberka la raacayo; marka 100 wareeg waa ku dhawaad tuurista lacag birta ah. Jilayaasha goobtan waxay hal ilbiriqsi ku socodsiiyaan 2,000 fadhi oo dhererka aad doorato ah, taasoo ah caddayn ka badan markhaati kasta.
Qaacido
Su'aalo
ItimaalkaxisaabItimaalFursadda natiijo, 0 ilaa 1 ama 0% ilaa 100%. Hal lambar: 1/37 = 2.70%.Akhri dhammaan → inaad mar kale faa'iido ku jirto wuxuu u dhacaa xagga eber marka aad ciyaarto. Wadartu way hoos u sii socotaa xad la'aan.
Maya. Waxay ka dhigan tahay in isbeddelladii hore ay noqdaan jajab ka yar tusaale ka weyn.
Lacag isle'eg, qiyaastii 10,000 ka hor inta faa'iidada kasiinadu si cad u muuqan. Hal lambar, qiyaastii 50,000.
Madadaalo Xisaabeed
Marka hore adigu isku day. Xal kasta waa qarsoon yahay; fur marka aad diyaar u tahay.
Laba saaxiib ayaa ciyaara 20 wareeg oo ciyaar caddaalad ahxisaabCiyaar caddaalad ahCiyaar aan dhinacna faa'iido lahayn: sharad kastaa wuxuu leeyahay qiime la filayo oo eber ah.Akhri dhammaan →, tuuris lacag-qadaadiic ama casaansharadCasaanSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee casaanka ah. Faransiis: rouge.Akhri dhammaan → iyo madowsharadMadowSharad lacag isle'eg ah oo ku saabsan 18-ka lambar ee madow. Faransiis: noir.Akhri dhammaan → iyadoo eberradagiraangirEberHal godka cagaaran ee aan daboolin sharad lacag isle'eg ah, dersin ama tiir; isha faa'iidada kasiinada. Sidoo kale: single zero, 0.Akhri dhammaan → la celiyo, waxayna hayaan dhibcaha socda. Tiri wareegyada mid kasta uu hormoodka yahay (barbarro waxaa loo tiriyaa kii hormoodka ahaa wax yar ka hor). Kee ayaa itimaal badan: in hormoodnimada loo qaybiyo 10 wareeg iyo 10, mise in hal saaxiib uu hormoodka ahaado dhammaan 20-ka?
Muuji xalka
Jawaab In hal saaxiib uu hormoodka ahaado dhammaan 20-ka wareeg ayaa aad uga itimaal badan: 35.2%, iyadoo labada saaxiib la tirinayo, marka loo eego 6.1% ee qaybsiga siman 10 iyo 10.
Fursadda in dhibcaha socda ee ciyaar caddaalad ahi ay siman yihiin 2k wareeg kadib waa u = C(2k, k)/2²ᵏ: 0.246 10 wareeg kadib iyo 0.176 20 kadib. Natiijo caan ah, sharciga arc-sine, waxay leedahay fursadda in saaxiib la magacaabay uu hormoodka ahaado si sax ah 2k ka mid ah 2n wareeg waa u(2k) × u(2n − 2k).
Hormoodka dhammaan 20-ka: u(20) × u(0) = 0.176 saaxiib kasta, 35.2% midkood. Qaybsi siman: u(10) × u(10) = 0.246² = 6.1%, qaybsiga ugu itimaalka yar dhammaan.
Sidaa darteed ciyaar caddaalad ah hormoodnimadu dhif ayay gacmaha u beddeshaa. Ciyaartoy hormoodka ahaa fiidka oo dhan, ama ka dambeeyay fiidka oo dhan, ma arkin wax aan caadi ahayn, waxba kama sheegayso giraangirta ama xirfadda. Epstein (2013) wuxuu isla sharcigan u bixiyaa ciyaaro dhaadheer: kala badh waqtiga, dhinaca nasiibka badani wuxuu hormoodka ahaadaa in ka badan 85% ciyaarta.
Kaftan yar
Celcelisku wuu isu soo dhowaadaa. Wadartu way iska tagtaa.
Ilaha
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.