Amlili deg uɣawas aɣezfan: alugen n wuṭṭunen imeqqranen deg rulit
Amek i yettqarrab ulemmas ɣer −2,70%, d wayɣer aya yettawi ugar n wakud n wayen i d-yeqqar uḥulfu.
Alemmas n lexsara i tuzzya yettqarrab ɣer −1/37 mi ara ttnernint tuzzyiwin, s usemres yettenqasen am 1/√N. Deffir 1 000 n tuzzyiwin ɣef uzeggaɣ, alemmas s umata yella daxel n ±3% seg wayen yettwaṛǧan.
Alugen n wuṭṭunen imeqqranen
Alemmas deg tikli n rrhun imanayen yettqarrab ɣer wazal yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk →. Deffir N n tuzzyiwin s lexlaṣ imsawi s yiwen uferdisidrimenAferdisRrehn agejdan s wacu i yettxeddem unagraw neɣ amurar. Inagrawen n usnerni ttwaglamen s yiferdisen akken ad ilin i yal ṭṭabla.Ɣer akk →, agmuḍ alemmas i tuzzya yesɛa azal yettwaṛǧan n −1/37 d ubeɛɛed alugantusnaktAbeɛɛed aluganAẓar amkuẓ n tavaryans; ameccaq n umata gar ugmuḍ d wazal yettwaṛǧan.Ɣer akk → n 1/√N. Deg N = 100, asemres-nni d 10% n udrim n rrehn, qrib ukkuẓ n tikkal 2,7% n tezmilt. Deg N = 1 000 d 3,2%, qrib kif kif d tezmilt. Deg N = 10 000 d 1%, lmaziyya tban-d s lebyan. Lmaziyya ur d-tettban ara deg teɣimit, tettban-d s tidet deg useggas.
Ayen yettqarraben d wayen ur nettqarrab ara
Alemmas i tuzzya yettqarrab. Amḍan meṛṛa ala: yettbeɛɛid ugar ɣef yilem mi ara yimɣur N, s qrib 2,7% n N deg wayen yettwaṛǧan, s usemres n √N i d-yezzin i waya. Amurar i yuraren 10 000 n tuzzyiwin s $10 yettwaṛǧan ad yili s lexsara n $2 700, rnu neɣ kkes $1 000. Tafesna deg tikli n uzeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → tersa zik qrib 48,65%; lḥisab deg tikli ur yers ula s anida.
- p10 −$440
- p25 −$280
- azal n tlemmast −$140
- p75 +$0
- p90 +$140
Ayɣer yettecceḍ uḥulfu
Imdanen ttraǧun lmaziyya ad d-tban s tɣawla acku 2,70% yettban d aṭas, ttraǧun izrar iɣezfanen ad «msawan» acku alugen n wuṭṭunen imeqqranentusnaktAlugen n wuṭṭunen imeqqranenAlemmas n yigmaḍ imanayen yettqerrib ɣer wazal yettwaṛǧan mi ara yettimɣur umḍan n tirmitin.Ɣer akk → yeqqar belli ilemmasen ttqarraben. Sin yiḥulfa-a ɣelṭen deg teskala: lmaziyya d tamecṭuḥt mgal 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 → n yiwet n tuzzya (σ = 1 n uferdis mgal EV = 0,027), ihi tettawi (1/0,027)² ≈ 1 400 n tuzzyiwin akken ad d-tban s yiwen sigma. Yerna aqarreb n ulemmas ur yettɛawan ara akken ad d-yerr amḍan meṛṛa; yessfesay kan ahuzzu yezrin.
Aqarreb i rrhun nniḍen
I yiwen wuṭṭunrrehnYiwen wuṭṭunYiwen wuṭṭun kan, ixelleṣ 35:1.Ɣer akk → σ = 5,84, ihi yiwen leḥsab yettak-d (5,84/0,027)² ≈ 47 000 n tuzzyiwin akken lmaziyya ad taweḍ ɣer yiwen sigma. Amurar ɣef yiwen wuṭṭun yezmer ad yurar iseggasen war ma lmaziyya tettwafraq ɣef zzher deg yiseklasen-is, ɣas akken ixelleṣ yiwet n 2,70% am umurar n uzeggaɣ i tt-iwalan deg kra n ddurtat.
Ayen d-yettawi i ukayad n yinagrawen
Yal win yeqqaren belli anagraw yeteddu ilaq ad yezmer ad t-id-yesken deg 10 000 n tuzzyiwin neɣ ugar s ulemmas sennig n yilem yettwarun. Deg 1 000 n tuzzyiwin, alemmas sennig n yilem ɣef lexlaṣ imsawi d aneḍru n yiwen seg semmus ma ulac lmaziyya; deg 100 n tuzzyiwin d qrib aḍeggeṛ n uṣurdi. Isimulaturen n usmel-a sselkamen 2 000 n tɣimiyin s teɣzi i tfernem deg yiwet n tsint, d abeggen ugar n yal awal n yimdanen.
Tasemselt
Isteqsiyen
TaprubabilittusnaktTaprubabilitAzal n yiwen ugmuḍ ad d-yeḍru, seg 0 ɣer 1 neɣ seg 0% ɣer 100%. Yiwen wuṭṭun: 1/37 = 2,70%.Ɣer akk → ad tilim tikkelt nniḍen s rrbeḥ tettṣubbu ɣer yilem mi ara turarem. Amḍan meṛṛa yettṣubbu war talast.
Ala. Yebɣa ad yini belli ahuzzu yezrin yettuɣal d aḥric amecṭuḥ n tegrumma tameqqrant ugar.
I lexlaṣ imsawi, qrib 10 000 uqbel ad d-tban lmaziyya s lebyan. I yiwen wuṭṭun, qrib 50 000.
Urar s tusnakt
Ɛerḍet-tent s yiman-nwen qbel. Yal tifrat tettwaffer; ldit-tt mi ara tilim twejdem.
Sin yimdukal urarn 20 n tunnḍiwin n wurar n lḥeqqtusnaktUrar n lḥeqqUrar anda ulac win ɣur-s lmaziyya: yal rrehn azal-is yettwaṛǧan d ilem.Ɣer akk →, tigri n uṣurdi neɣ azeggaɣrrehnAzeggaɣRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen izeggaɣen. S tefransist: rouge.Ɣer akk → mgal uberkanrrehnAberkanRrehn s lexlaṣ imsawi ɣef 18 n wuṭṭunen iberkanen. S tefransist: noir.Ɣer akk → s yilmawenaḍebsiIlemTaxxamt tazegzawt tasuft ur yeṭṭif ula d yiwen n rrehn s lexlaṣ imsawi, n ddzina neɣ n tgejdit; d aɣbalu n lmaziyya n lkazinu. Daɣen: yiwen yilem, 0.Ɣer akk → i d-yettuɣalen, u ttarun tanqiḍt i yettkemmilen. Ḥesbet tunnḍiwin anda yal yiwen yezwar (amsawi yettwaḥseb i win yezwaren qbel). Anwa i yezmren ugar: ad yezwir yal yiwen, 10 n tunnḍiwin ɣef 10, neɣ ad yezwir yiwen umdakkel 20-nni meṛṛa?
Sken-d tifrat
Tiririt Yiwen umdakkel i yezwaren 20-nni n tunnḍiwin yezmer ugar aṭas: 35,2%, s yal yiwen seg yimdukal, mgal 6,1% i 10 ɣef 10 imsawi.
Taprubabilit ad tili tenqiḍt n lḥeqq d tamsawit deffir 2k n tunnḍiwin d u = C(2k, k)/2²ᵏ: 0,246 deffir 10 n tunnḍiwin d 0,176 deffir 20. Agmuḍ aklasiki, alugen arc-sine, yenna belli taprubabilit ad yezwir yiwen umdakkel yettwasemman 2k n tunnḍiwin s tidet seg 2n d u(2k) × u(2n − 2k).
Azwar deg 20-nni meṛṛa: u(20) × u(0) = 0,176 i yal amdakkel, 35,2% i yal yiwen seg-sen. Abeṭṭu imsawi: u(10) × u(10) = 0,246² = 6,1%, abeṭṭu i yesɛan taprubabilit tamecṭuḥt akk.
Ihi deg wurar n lḥeqq, drus i yettbeddil win yezwaren. Amurar yezwaren tameddit meṛṛa, neɣ yellan deffir tameddit meṛṛa, ur iwala acemma n wuzzig, u ayagi ur d-yettini acemma ɣef uḍebsi neɣ ɣef tzmert. Epstein (2013) yefka-d alugen-nni yiwen i wuraren iɣezfanen ugar: azgen n wakud tama yesɛan zzher ugar tezwar ugar n 85% n wurar.
Taḍsa i usgunfu
Alemmas yettqarrab. Amḍan meṛṛa yettruḥ kan.
Iɣbula
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.