Abeɛɛed alugan deg rulit
Abeɛɛed alugan n rulit, aẓar amkuẓ n tavaryanstusnaktTavaryansAktazal n wamek i d-ttwazzaren igmaḍ i tama n wazal yettwaṛǧan. Meqqret i rrehn ɣef yiwen wuṭṭun, meẓẓiyet i rrhun s lexlaṣ imsawi.Ɣer akk →, d ameccaq s umata gar ugmuḍ d wayen yettwaṛǧan.
I yal $1 yettwarehnen, σ d 5,84 i yiwen wuṭṭun d 1,00 i uzeggaɣ. Sgutet s udrim n rrehn d uẓar amkuẓ n umḍan n tuzzyiwin i teɣimit.
Alugen n ufus
Qrib sin seg kraḍ n tɣimiyin ttaweḍent daxel n yiwen σ seg wayen yettwaṛǧan, 95% daxel n sin. I 100 n tuzzyiwin ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → s $10 (yettwaṛǧan −$27, σ = $100) tugget n tɣimiyin ttɣimint gar −$127 d +$73, qrib akk gar −$227 d +$173. Agmuḍ beṛṛa n wagraw-a mačči d abeggen n wacemma ala belli yiwet n teɣimit seg ɛecrin txeddem-it.
Ayɣer √N
Lexsara yettwaṛǧantusnaktLexsara yettwaṛǧanAzal yettwaṛǧan seg tmerna n yidrimen yettwarhen; d alemmas n wayen yettwaxsar deg yiwet n tɣimit neɣ deg yiwen wakud.Ɣer akk → tettnerni s tfesna n N; asemres yettnerni s tfesna n √N. I N amecṭuḥ, asemres d netta i yɣelben, tiɣimiyin d aḍeggeṛ n uṣurdi s umyal amecṭuḥ. I N ameqqran, lexsara tezgar asemres. Tanaddit n umlili, anda lexsara yettwaṛǧan tegda yiwen ubeɛɛed alugantusnaktAbeɛɛed aluganAẓar amkuẓ n tavaryans; ameccaq n umata gar ugmuḍ d wazal yettwaṛǧan.Ɣer akk →, tella deg N = (σ/lmaziyya)² = (1/0,027)² ≈ 1 370 n tuzzyiwin i lexlaṣ imsawi d (5,84/0,027)² ≈ 46 800 i yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk →. Ddaw n yimḍanen-a, d zzher i yefran; nnig-sen, d lmaziyya.
Aseqdec-is
Akken ad tẓerm ma taɣimit tesweḥcay, ḥesbet (agmuḍ − EV)/σ. Amurar n $10 ɣef uzeggaɣ i yekfan 100 n tuzzyiwin s +$150 yella deg (150 + 27)/100 = 1,77σ, d agmuḍ n yiwen seg 25: d zzher, mačči d ayen yesweḥcen. Amurar ɣef yiwen wuṭṭun s yiwen +$150 yella deg 0,3σ: d iḍ am wiyaḍ. Yiwen ugmuḍ s yidularen yebɣa ad yini ayen yemgaraden ɣef rrhun yemgaraden.
Tuccḍa talugant n ufmiḍi
Yiwen leḥsab yeqqar-awen acḥal n tuzzyiwin i ilaqen akken ad twalim lmaziyya deg yisefka. Tuccḍa talugant n ufmiḍi n rrbeḥ yettwalan d √(p(1 − p)/N). I uzeggaɣ s N = 1 000: √(0,4865 × 0,5135 / 1000) ≈ 1,6%. Ameccaq gar uṣurdi imsawi d uzeggaɣ d 1,35%, ihi deffir 1 000 n tuzzyiwin ur tezmirem ara ad ten-tferqem s laman. Deffir 10 000 tuccḍa talugant d 0,5%, tzemrem. D ayagi daɣen i yerran tifin n umyal n uḍebsi tesra aṭas n tuzzyiwin.
Ɣur-wen i umyal n ubeṭṭu
Igmaḍ n yiwen wuṭṭun mačči d abeṭṭu amagnu deg teɣimit tawezlant: tugget n tɣimiyin d −$10 i tuzzya s tineggzin n +$350 seg wakud ɣer wayeḍ. Alugen ±1σ yeglam asemres akken iwata, maca talɣa ur tt-yeglam ara akken iwata alamma N yewweḍ timiḍiwin. I rrhun s lexlaṣ imsawirrehnRrehn s lexlaṣ imsawiAzeggaɣ/aberkan, aryan/uyug, afellay/adday. 18 n wuṭṭunen, ixelleṣ 1:1.Ɣer akk →, aqarreb amagnu yelha seg qrib 30 n tuzzyiwin.
Tasemselt
Isteqsiyen
D abeggen belli turarem qrib 40 n tɣimiyin, neɣ tellam deg tin n zzher seg ṛebɛin. Ɛawdet-itt.
Yettbeddil drus, drus: tuccḍa talugant n ulemmas d σ/√N. Deg N = 10 000 d 1% n udrim n rrehn.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Deg 100 n tuzzyiwin n uḍebsi awrupi, yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk → ɣef uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → yella deg rrbeḥ s 51 n rrbeḥ ma drus, u yiwen n uferdis ɣef yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → yella deg rrbeḥ ma yeffeɣ-d wuṭṭun-is ma drus 3 n tikkal. Seqdecet taznagt n uqelwac akken ad tḥesbem s tmuɣli snat-nni n tprubabiliyin, syin serwset-tent s tririyin tiṣeḥḥa.
Sken-d tifrat
Tiririt Azeggaɣ: taznagt n uqelwac tettak-d 35,6% u tiririt tuṣḥiḥt d 35,5%. Yiwen wuṭṭun: taznagt n uqelwac tettak-d 55,0% u tiririt tuṣḥiḥt d 50,9%. Abrid awezlan yeddu i uzeggaɣ u yeɣleḍ i yiwen wuṭṭun.
Azeggaɣ: alemmas n rrbeḥ d 100 × 18/37 = 48,6, s uzerreɛ n √(100 × 18/37 × 19/37) = 5,0. Deg rrbeḥ yebɣa ad yini 51 neɣ ugar; talemmast, 50,5, tella 0,37 n uzerreɛ nnig walemmas, u taznagt n uqelwac tessers 35,6% nnig-s. Timerna n tprubabiliyin tiṣeḥḥa n 51, 52 … 100 n rrbeḥ tettak-d 35,5%.
Yiwen wuṭṭun: alemmas n tuɣliwin d 100/37 = 2,70, s uzerreɛ n √(100 × 1/37 × 36/37) = 1,62. Kraḍ n tuɣliwin neɣ ugar yebɣa ad yini nnig 2,5, 0,12 n uzerreɛ ddaw walemmas: 55,0% s teznagt n uqelwac. S tidet, d 1 ma nekkes tiprubabiliyin n 0, 1 d 2 n tuɣliwin, 6,5% + 17,9% + 24,7%, ayen yeǧǧan 50,9%.
Taznagt n uqelwac tesra aṭas n yigmaḍ ɣef snat n tama n walemmas. Azeggaɣ yesɛa-ten deffir 100 n tuzzyiwin; uṭṭun i d-yeffɣen ddaw kraḍ n tikkal s ulemmas ur ten-yesɛi ara. Taznagt tettak-d ula d 8,7% i «ulac tuɣli», anda taprubabilit n tidet d 6,5%. Taylor (2021) yesserset abinumyal d teznagt n uqelwac yiwen ɣer tama n wayeḍ s yiwet n tarrayt.
Taḍsa i usgunfu
Yiwet n teɣimit seg ɛecrin tella beṛṛa n sin sigma. Yella yal tikkelt win yellan deg ujeḥnuḍ.
Iɣbula
- 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.