Seerndu Ndenndaandu e Ruleet
Seerndu ndenndaandu ruleet, daɗol kaaree wariyaasmatematikWariyaasPeeta no njeñtuɗi saŋkitiri e njaru fodaandu. Ina toowi ngam limoore wootere, ina lesɗi ngam pariiji njoɓdi fotndi.Tar fof →, ko woɗɗeende aadanteende hakkunde njeñtudi e ko fodaa.
E kala $1 pariyaaɗo, σ ko 5,84 e limoore wootere e 1,00 e boɗeere. Fiɓ ɗum e pari e daɗol kaaree limoore taarle ngam jonnde.
Sariya newɗo
Hedde feccere ɗiɗi e nder tati jonɗe ina ndaroo nder σ gootal ko fodaa, 95% kadi nder ɗiɗi. E taarle 100 boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → e $10 (fodaa −$27, σ = $100) jonɗe ɓurɗe heewde ina ngona hakkunde −$127 e +$73, hedde fof kadi hakkunde −$227 e +$173. Njeñtudi yaltiindi ndeen keerol hollataa hay huunde si wonaa wonde jonnde wootere e nder noogas ina waɗa ɗum.
Ko waɗi √N
Majjere fodaandematematikMajjere fodaandeNjaru fodaandu fiyaandu e kaalis pariyaaɗo fof; ko hakkundeere kaalis majjataako nder jonnde walla nder sahaa.Tar fof → ina ɓeydoo e nder N; caggitagol ina ɓeydoo e nder √N. Nde N famɗi, caggitagol ina ɓura doole, jonɗe ko hono feccere-feccere ooñiinde seeɗa. Nde N mawni, majjere ina ɓura caggitagol. Nokku ɓennugol, ɗo majjere fodaande fotata e seerndu ndenndaandumatematikSeerndu ndenndaanduRaasin karee wariyaas; ko woɗɗeende aadanteende njeñtudi e njaru fodaandu.Tar fof → wootere, ko N = (σ/ɓural)² = (1/0,027)² ≈ 1 370 taarle e njoɓdi fotndi e (5,84/0,027)² ≈ 46 800 e limooje wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof →. Les ɗee limooje, ko sahaa taƴata; dow majji, ko ɓural ngal.
Huutoraade ɗum
Ngam anndude si jonnde ko huunde ceerunde, hiis (njeñtudi − EV)/σ. Fijoowo waɗoowo pari $10 e boɗeere timmini taarle 100 e +$150 ina woni e (150 + 27)/100 = 1,77σ, njeñtudi wootere e nder 25: sahaa moƴƴo, wonaa kaawniika. Fijoowo limoore wootere e +$150 gootun ina woni e 0,3σ: jemma aadanteejo. Njeñtudi dolaar wootere ina firta huuɗe ceertuɗe e pariiji ceertuɗi.
Juumre ndenndaande feccere
Limto gootol ngol ina hollaa no taarle foti ngam yi’ude ɓural ngal e keɓe ɗee. Juumre ndenndaande feccere dañe yiyaande ko √(p(1 − p)/N). E boɗeere e N = 1 000: √(0,4865 × 0,5135 / 1000) ≈ 1,6%. Ceergal hakkunde pees kaalis potɗo e boɗeere ko 1,35%, ɗuum waɗi caggal taarle 1 000 a waawataa tawo seerndude ɗum e hoolaare. Caggal 10 000 juumre ndenndaande ko 0,5% tawa a waawii. Ɗum kadi woni ko waɗi yiytude ooñol taarorde ina sokli taarle keewɗe no feewi.
Reenaade ooñol
Njeñtuɗi limoore wootere ina woɗɗi senndugol normal e jonnde gaɗaande: jonɗe ɓurɗe heewde ko −$10 tabitngo e kala taarol e diwal +$350 e sahaaji. Sariya ±1σ ina sifoo caggitagol ngol no feewi kono mbaadi ndi no moƴƴaani haa N hewta teemedde. E pariiji njoɓdi fotndipariPari njoɓdi fotndiBoɗeere/ɓaleere, peccotaake/peccotoonde, mawɗe/tokooseeje. Limooje 18, ina yoɓa 1:1.Tar fof →, hedde normal ngal ina moƴƴi gila taarle 30 hedde.
Formil
Naamne
Ko seedee wonde a fijii hedde jonɗe 40, walla a wonii e wootere jonnde sahaa e nder capanɗe nay. Fuɗɗito ɗum.
Ina ɓura famɗude jaaɓagol: juumre ndenndaande hakkundeere ko σ/√N. E N = 10 000 ko 1% pari.
Weltaare e Matematik
Etu ɗum hoore maa adii. Kala jaabawol ina suuɗii; uddit ɗum so a heblii.
E taarle 100 taarorde Orop, initekaalisInitePari fuɗɗoode mo sistem walla fijoowo gollirta. Jokkondirɗe pari ina cifee e initeeji ngam ɗi kuutoroo e kala taabal.Tar fof → wootere e boɗeerepariBoɗeerePari njoɓdi fotndi e limooje 18 boɗeeje. E Farayse: rouge.Tar fof → ina woni e dañal so dañii 51 tal, inite wootere e limoore wooterepariLimoore wootereLimoore wootere tan, ina yoɓa 35:1.Tar fof → ina woni e dañal so limoore mum yaltii laabi 3 tal. Huutoro kuurtol Gauss ngam hiinnaade porobabilite ɗiɗi ɗee, ndeen yerondir ɗe e jaabawuuji goonga ɗii.
Hollu jaabawol ngol
Jaabawol Boɗeere: kuurtol Gauss ina addi 35,6%, jaabawol goonga ngol ko 35,5%. Limoore wootere: kuurtol Gauss ina addi 55,0%, jaabawol goonga ngol ko 50,9%. Laawol ɓadngol ngol ina golla ngam boɗeere ina juuma ngam limoore wootere.
Boɗeere: dañe ɗee ina njogii hakkundeere 100 × 18/37 = 48,6, e senndugol √(100 × 18/37 × 19/37) = 5,0. Wonde e dañal ko 51 walla ko ɓuri; maande hakkundeere, 50,5, ko senndugol 0,37 ɓurngol hakkundeere ndee, kuurtol Gauss ina waɗa 35,6% dow ɗum. Ɓeydude porobabilite goonga dañe 51, 52 … 100 ina addi 35,5%.
Limoore wootere: hawrugol ina jogii hakkundeere 100/37 = 2,70, e senndugol √(100 × 1/37 × 36/37) = 1,62. Hawrugol tati walla ko ɓuri ina firta dow 2,5, senndugol 0,12 les hakkundeere ndee: 55,0% e kuurtol Gauss. E goonga, ko 1 ustaa porobabilite hawrugol 0, 1 e 2, 6,5% + 17,9% + 24,7%, ɗum ina acca 50,9%.
Kuurtol Gauss ina naamnoo njeñtuɗi keewɗi e ɓerɗe ɗiɗi hakkundeere ndee. Boɗeere ina jogii ɗi caggal taarle 100; limoore hawrata ko ɓuri famɗude laabi tati e hakkundeere jogaani ɗi. Kuurtol ngol ina rokka hay 8,7% “alaa hawrugol”, tawa porobabilite goonga ndee ko 6,5%. Taylor (2021) ina waɗa binomiyal e kuurtol Gauss ɓerɗe e ɓerɗe e laawol gootol ngol.
Ƴeewndo weltinoowo
Jonnde wootere e nder noogas ina yaltii sigma ɗiɗi. Kala sahaa woodi gooto e geɗal sakkitiingal.
Iwdi
- 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.