Kuswedera kweNguva Refu: Mutemo weNhamba Huru muRoulette
Kuti avhareji inogadzikana sei ichienda kusvika −2.70%, uye kuti nei izvozvo zvichitora nguva yakareba kupfuura zvinofungwa nevanhu.
Avhareji yekurasikirwa pakutenderera kwega kwega inoswedera kusvika −1/37 sezvo kutenderera kuchiwanda, nekupararira kunoderera sa1/√N. Mushure mekutenderera 1,000 pane tsvuku, avhareji inowanzova mukati me±3% yezvinotarisirwa.
Mutemo wenhamba huru
Avhareji inofamba yemabheti akazvimirira inoenda kukukosha kunotarisirwamasvomhuKukosha kunotarisirwaMhedzisiro yepakati pabheti rimwe nekufamba kwenguva refu. −1/37 yemari yakabhejwa pabheti rimwe nerimwe reEurope rakajairwa.Verengai zvese →. Mushure mekutenderera N kwemabheti emubhadharo wakaenzana payunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → imwe, avhareji yemhedzisiro pakutenderera ine zvinotarisirwa zviri −1/37 nestandard deviationmasvomhuStandard deviationMudzi wesikweya wemusiyano; chinhambwe chakajairwa chemhedzisiro kubva pakukosha kunotarisirwa.Verengai zvese → ye1/√N. Pa N = 100 kupararira ikoko i10% yemari yakabhejwa, kunenge kana kana chiratidzo che2.7%. Pa N = 1,000 i3.2%, kunenge kwakaenzana nechiratidzo. Pa N = 10,000 i1%, uye chikamu chekasino chinoonekwa zvakajeka. Chikamu chekasino hachioneki musesheni imwe, asi hachigoni kurambwa mugore rimwe.
Zvinoswedera nezvisingaswederi
Avhareji pakutenderera inoswedera. Huwandu hwose hahuswederi: hunoramba huchibva kure ne zero sezvo N ichikura, nekunenge 2.7% yaN muzvinotarisirwa, nekupararira kwe√N kwakapoteredza ipapo. Mutambi akatamba kutenderera 10,000 pa$10 anotarisirwa kuve arasikirwa ne$2,700, kuwedzera kana kubvisa $1,000. Chikamu chinofamba chenhamba tsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → chakagadzikana kare pedyo ne48.65%; mari yasara haina kumbogadzikana chero kupi.
- p10 −$440
- p25 −$280
- median −$140
- p75 +$0
- p90 +$140
Kuti nei pfungwa dzevanhu dzichikanganisa
Vanhu vanotarisira kuti chikamu chekasino chionekwe nekukurumidza nekuti 2.70% inonzwika sezvizhinji, uye vanotarisira kuti mitsara mirefu “ienzane” nekuti mutemo wenhamba hurumasvomhuMutemo wenhamba huruAvhareji yemhedzisiro yakazvimirira inoswedera kukukosha kunotarisirwa sezvo huwandu hwekuedza huchikura.Verengai zvese → unoti maavhareji anoswedera. Pfungwa dzose idzi dzinokanganisa saizi: chikamu chekasino chidiki kana chichienzaniswa nemusiyanomasvomhuMusiyanoChiyero chekuti mhedzisiro yakapararira zvakadii kutenderedza kukosha kunotarisirwa. Wakakwirira pastraight up, wakaderera pamabheti emubhadharo wakaenzana.Verengai zvese → wekutenderera kumwe (σ = yuniti 1 ichienzaniswa neEV = 0.027), saka zvinotora (1/0.027)² ≈ kutenderera 1,400 kuti chioneke pasigma imwe. Uye kuswedera kweavhareji hakuiti chinhu kudzosa huwandu hwose; kunongodzikisa simba remisiyano yakapfuura.
Kuswedera kwemamwe mabheti
Pastraight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese → σ = 5.84, saka kuverenga kumwe chete ikoku kunopa (5.84/0.027)² ≈ kutenderera 47,000 kuti chikamu chekasino chisvike pasigma imwe. Mutambi westraight up anogona kutamba kwemakore pasina chikamu chekasino chinosiyaniswa nemhanza mumarekodhi ake, achibhadhara 2.70% chaiyo yakafanana nemutambi wetsvuku anochiona mukati memavhiki.
Zvazvinoreva pakuedza masisitimu
Ani nani anoti sisitimu inoshanda anofanira kukwanisa kuzviratidza pakutenderera 10,000 kana kupfuura neavhareji yakanaka yakanyorwa. Pakutenderera 1,000, avhareji yakanaka pamubhadharo wakaenzana chiitiko chimwe chete pashanu pasi pe null hypothesis; pakutenderera 100 chinenge kukanda mari. Masimulator ari pawebhusaiti ino anotamba masesheni 2,000 ekureba kwamasarudza musekondi imwe, uye ihwo humbowo hwakawanda kupfuura chero uchapupu hwemunhu.
Fomula
Mibvunzo
MukanamasvomhuMukanaMukana wemhedzisiro, kubva pa0 kusvika pa1 kana 0% kusvika 100%. Nhamba imwe: 1/37 = 2.70%.Verengai zvese → wekuzombovawo mberi zvakare unoderera uchienda kuzero sezvamunoramba muchitamba. Huwandu hwose hunoramba huchidzika pasina muganho.
Kwete. Unoreva kuti misiyano yakapfuura inova chikamu chidiki chesampuru huru.
Pamubhadharo wakaenzana, kunenge 10,000 chikamu chekasino chisati choonekwa zvakajeka. Pastraight up, kunenge 50,000.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Shamwari mbiri dzinotamba matanho 20 emutambo wakaenzanamasvomhuMutambo wakaenzanaMutambo usina divi rine mukana: bheti rimwe nerimwe rine kukosha kunotarisirwa kwe zero.Verengai zvese →, kukanda mari yesimbi kana tsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → ichipikisa nhemabhetiNhemaBheti remubhadharo wakaenzana panhamba 18 nhema. ChiFrench: noir.Verengai zvese → mazerovhiriZeroGomba rimwe chete rakasvibira risingafukidzwi nebheti remubhadharo wakaenzana, redozeni kana rekoramu; ndiko kunobva chikamu chekasino. Mamwe mazita: zero imwe, 0.Verengai zvese → achidzoserwa, uye dzinochengeta mhedzisiro iri kuenderera. Verengai matanho ayo mumwe nemumwe ari mberi (kuenzana kunoverengerwa uya anga ari mberi pamberi pazvo). Chii chine mukana mukuru: kuti kutungamira kugoverwe matanho 10 ne10, kana kuti shamwari imwe itungamire ose 20?
Ratidza mhinduro
Mhinduro Shamwari imwe kutungamira matanho ose 20 kune mukana mukuru zvikuru: 35.2%, tichiverenga shamwari ipi neipi, kana zvichienzaniswa ne6.1% pakuenzana kwe10 ne10.
Mukana wekuti mhedzisiro yakaenzana iri kuenderera ive yakaenzana mushure mematanho 2k i u = C(2k, k)/2²ᵏ: 0.246 mushure mematanho 10 ne0.176 mushure me20. Mhedzisiro yakakurumbira, arc-sine law, inoti mukana wekuti shamwari imwe yakadomwa itungamire matanho 2k chaiwo pa2n i u(2k) × u(2n − 2k).
Kutungamira ose 20: u(20) × u(0) = 0.176 pashamwari imwe neimwe, 35.2% peipi neipi. Kugovana zvakaenzana: u(10) × u(10) = 0.246² = 6.1%, kugovana kune mukana mudiki kupfuura kwose.
Saka mumutambo wakaenzana kutungamira kunowanzosachinja maoko. Mutambi anga ari mberi manheru ose, kana shure manheru ose, haana kuona chinhu chisina kujairika, uye hazvitauri chinhu nezvevhiri kana unyanzvi. Epstein (2013) anopa mutemo mumwe chete uyu pamitambo mirefu: hafu yenguva divi rine rombo rinotungamira kupfuura 85% yekutamba.
Kuseka zvishoma
Avhareji inoswedera. Huwandu hwose hunongoenda hwega.
Zvinyorwa
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.