Umgama oqhelekileyo (standard deviation) kwi-roulette
Ukutenxa okuqhelekileyo (standard deviation) kwi-roulette, ingcambu yesikwere yokwahlukaizibaloUkwahlukaUmlinganiselo wokuba iziphumo zisasazeke kangakanani zijikeleze ixabiso elilindelekileyo. Kuphezulu kwibheji yenani elinye, kuphantsi kwiibheji zemali elinganayo.Funda yonke →, ngumgama oqhelekileyo phakathi kwesiphumo nesiphumo esilindelekileyo.
Nge-$1 ebhejiweyo, i-σ yi-5.84 kwinani elinye kunye ne-1.00 kobomvu. Phindaphinda ngebheji nangengcambu yesikwere yenani lemijikelo ukuze ufumane eyeseshoni.
Umthetho olula
Malunga nesibini kwisithathu seeseshoni ziphela ngaphakathi kwe-σ enye ukusuka kwisiphumo esilindelekileyo, kwaye i-95% ngaphakathi kwezimbini. Kwimijikelo eli-100 kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → nge-$10 (kulindeleke −$27, σ = $100) uninzi lweeseshoni luwela phakathi kwe-−$127 ne-+$73, kwaye phantse zonke phakathi kwe-−$227 ne-+$173. Isiphumo esingaphandle kolo luhlu asibubungqina bayo nantoni na, ngaphandle kokuba iseshoni enye kumashumi amabini iyakwenza oko.
Kutheni √N
Ilahleko elindelekileyoizibaloIlahleko elindelekileyoIxabiso elilindelekileyo liphindwe ngesixa esipheleleyo esibhejiweyo; isixa esiphakathi esilahlekayo kwiseshoni okanye kwixesha elithile.Funda yonke → ikhula ngokomlinganiselo ka-N; ukusasazeka kukhula ngokomlinganiselo ka-√N. Xa u-N emncinci, ukusasazeka kuyalawula kwaye iiseshoni zifana nokuphosa ingqekembe ngokuthambekela okuncinci. Xa u-N emkhulu, ilahleko iyakudlula ukusasazeka. Indawo yokuwelana, apho ilahleko elindelekileyo ilingana nokutenxa okuqhelekileyoizibaloUkutenxa okuqhelekileyo (standard deviation)Ingcambu yesikwere yokwahluka; umgama oqhelekileyo wesiphumo ukusuka kwixabiso elilindelekileyo.Funda yonke → okukanye, ikwi-N = (σ/inzuzo)² = (1/0.027)² ≈ imijikelo eyi-1,370 kwimali elinganayo kunye ne-(5.84/0.027)² ≈ 46,800 kwiibheji zenani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke →. Ngaphantsi kwala manani, ithamsanqa liyagqiba; ngaphezu kwawo, yinzuzo yekhasino egqibayo.
Ukuyisebenzisa
Ukugweba ukuba iseshoni ibingaqhelekanga na, bala (isiphumo − EV)/σ. Umdlali obheja i-$10 kobomvu ogqiba imijikelo eli-100 ku-+$150 ukwi-(150 + 27)/100 = 1.77σ, isiphumo esinye kwama-25: unethamsanqa, akumangalisi. Umdlali obheja kwinani elinye kwa-+$150 efanayo ukwi-0.3σ: ubusuku obuqhelekileyo. Isiphumo esifanayo ngeedola sithetha izinto ezahlukeneyo kwiibheji ezahlukeneyo.
Impazamo eqhelekileyo yomlinganiselo
Olu balo lunye likuxelela ukuba kufuneka imijikelo emingaphi ukuze ubone inzuzo yekhasino kwidatha. Impazamo eqhelekileyo (standard error) yomlinganiselo wophumelelo obonwayo ngu-√(p(1 − p)/N). Kobomvu no-N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Umsantsa phakathi kwengqekembe efanelekileyo nobomvu yi-1.35%, ngoko emva kwemijikelo eli-1,000 akukabinakho ukuzahlula ngokuqiniseka. Emva kwe-10,000 impazamo eqhelekileyo yi-0.5% kwaye uyakwazi. Kungenxa yoko ukufumanisa ivili elithambekileyo kufuna imijikelo emininzi kangaka.
Isilumkiso malunga nokugoba
Iziphumo zenani elinye azisasazeki ngokuqhelekileyo (normal) kwiseshoni emfutshane: uninzi lweeseshoni lu-−$10 olungaguquguqukiyo kumjikelo ngamnye kunye nokutsiba kwe-+$350 ngamaxesha athile. Umthetho we-±1σ uchaza ukusasazeka ngokuchanekileyo kodwa ubume kakubi de u-N abe ngamakhulu. Kwiibheji zemali elinganayoibhejiIbheji yemali elinganayoObomvu/omnyama, angalinganiyo/alinganayo, aphezulu/aphantsi. Amanani ali-18, ihlawula u-1:1.Funda yonke → uqikelelo oluqhelekileyo lulungile ukusuka malunga nemijikelo engama-30.
Ifomula
Imibuzo
Bubungqina bokuba udlale malunga neeseshoni ezingama-40, okanye ubukwenye enethamsanqa kumashumi amane. Phinda kwakhona.
Ujija kancinci nangakumbi: impazamo eqhelekileyo yomndilili ngu-σ/√N. Xa u-N = 10,000 yi-1% yebheji.
Ukonwaba ngezibalo
Qala uzizame ngokwakho. Isisombululo ngasinye sisongiwe; sivule xa ukulungele.
Kwimijikelo eli-100 yevili laseYurophu, iyunithiimaliIyunithiIbheji esisiseko esetyenziswa yinkqubo okanye ngumdlali. Ukunyuswa kweebheji kuchazwa ngeeyunithi ukuze kusebenze kuyo nayiphi na itafile.Funda yonke → enye kobomvuibhejiObomvuIbheji yemali elinganayo kumanani ali-18 abomvu. NgesiFrentshi: rouge.Funda yonke → iphambili ngeempumelelo ezingama-51 ubuncinane, kwaye iyunithi enye kwinani elinyeibhejiInani elinyeInani elinye, ihlawula u-35:1.Funda yonke → iphambili ukuba inani layo liphuma ubuncinane izihlandlo ezi-3. Sebenzisa igophe lentsimbi ukuqikelela omabini amathuba, uze uwathelekise neempendulo ezichanileyo.
Bonisa isisombululo
Impendulo Obomvu: igophe lentsimbi linika i-35.6% kwaye impendulo echanileyo yi-35.5%. Inani elinye: igophe lentsimbi linika i-55.0% kwaye impendulo echanileyo yi-50.9%. Indlela emfutshane iyasebenza kubomvu kwaye iyaphosa kwinani elinye.
Obomvu: iimpumelelo zinomndilili we-100 × 18/37 = 48.6, nokusasazeka kwe-√(100 × 18/37 × 19/37) = 5.0. Ukuba phambili kuthetha ama-51 nangaphezulu; uphawu oluphakathi, 50.5, lungaphezulu komndilili ngokusasazeka okungu-0.37, kwaye igophe lentsimbi libeka i-35.6% ngaphezu koko. Ukudibanisa amathuba achanileyo eempumelelo ezingama-51, 52 … 100 kunika i-35.5%.
Inani elinye: ukuphuma kunomndilili we-100/37 = 2.70, nokusasazeka kwe-√(100 × 1/37 × 36/37) = 1.62. Ukuphuma kathathu nangaphezulu kuthetha ngaphezu kwe-2.5, ukusasazeka okungu-0.12 ngaphantsi komndilili: 55.0% ngegophe lentsimbi. Ngokuchanileyo, ngu-1 thabatha amathuba okuphuma ka-0, ka-1 naka-2, 6.5% + 17.9% + 24.7%, nto leyo eshiya i-50.9%.
Igophe lentsimbi lifuna iziphumo ezininzi kumacala omabini omndilili. Obomvu unazo emva kwemijikelo eli-100; inani eliphuma ngaphantsi kokathathu ngomndilili alinazo. Igophe linika ne-8.7% “ekungaphumi”, apho ithuba lokwenyani liyi-6.5%. U-Taylor (2021) ubeka i-binomial negophe lentsimbi ecaleni ngendlela efanayo.
Uncumo
Iseshoni enye kumashumi amabini ingaphandle kwe-sigma ezimbini. Kusoloko kukho umntu osemsileni.
Imithombo
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.