Standard Deviation muRoulette
Standard deviation muRoulette, square root yemusiyanomasvomhuMusiyanoChiyero chekuti mhedzisiro yakapararira zvakadii kutenderedza kukosha kunotarisirwa. Wakakwirira pastraight up, wakaderera pamabheti emubhadharo wakaenzana.Verengai zvese →, ndiro daro rakajairika pakati pemhedzisiro nezvainotarisirwa.
Pa$1 yakabhejwa, σ i5.84 pa straight up uye 1.00 patsvuku. Wanzai nemari yakabhejwa uye nesquare root yehuwandu hwekutenderera kuti muwane yesesheni.
Mutemo wenyore
Zvinenge zvikamu zviviri muzvitatu zvemasesheni zvinomhara mukati ma σ imwe kubva pazvinotarisirwa uye 95% mukati mepiri. Pakutenderera 100 patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → pa$10 (kunotarisirwa −$27, σ = $100) masesheni mazhinji anowira mumutsetse unobva −$127 kusvika +$73, uye anenge ese mumutsetse unobva −$227 kusvika +$173. Mhedzisiro iri kunze kwechikamu ichocho haisi humbowo hwechinhu kunze kwekuti sesheni imwe pamakumi maviri inozviita.
Sei √N
Kurasikirwa kunotarisirwamasvomhuKurasikirwa kunotarisirwaKukosha kunotarisirwa kwakapetwa nemari yose yakabhejwa; mari yepakati inorasika musesheni kana munguva yakati.Verengai zvese → kunokura zvichienderana neN; kupararira kunokura zvichienderana ne√N. PaN diki kupararira ndiko kunotonga, uye masesheni akaita sekukanda mari ine kurerekera kudiki. PaN huru kurasikirwa kunopfuura kupararira. Pakuchinjana, apo kurasikirwa kunotarisirwa kwaenzana nestandard deviationmasvomhuStandard deviationMudzi wesikweya wemusiyano; chinhambwe chakajairwa chemhedzisiro kubva pakukosha kunotarisirwa.Verengai zvese → imwe, ndipo N = (σ/chikamu chekasino)² = (1/0.027)² ≈ kutenderera 1,370 pamubhadharo wakaenzana uye (5.84/0.027)² ≈ 46,800 pamastraight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese →. Pasi penhamba idzodzo, rombo ndiro rinosarudza; pamusoro padzo, chikamu chekasino ndicho chinosarudza.
Kuishandisa
Kuti muone kana sesheni yanga isina kujairika, verengai (mhedzisiro − EV)/σ. Mubheji wetsvuku pa$10 anopedza kutenderera 100 ari pa+$150 ari pa(150 + 27)/100 = 1.77σ, mhedzisiro imwe pa25: rombo rakanaka, kwete chinoshamisa. Mubheji we straight up ari pa+$150 imwe chete ari pa0.3σ: manheru akajairika. Mhedzisiro yemadhora yakafanana inoreva zvinhu zvakasiyana pamabheti akasiyana.
Standard error yechikamu
Arithmetic imwe chete iyi inokuudzai kuti kunoda kutenderera kwakawanda sei kuti muone chikamu chekasino mudata. Standard error yechikamu chekukunda chinoonekwa i√(p(1 − p)/N). Patsvuku neN = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Musiyano pakati pemari yakarurama inokandwa netsvuku i1.35%, saka mushure mekutenderera 1,000 hamusati mavakugona kuzvisiyanisa nechivimbo. Mushure me10,000 standard error i0.5% uye munogona. Ndosaka kuona kutsauka kwevhiri kuchidawo kutenderera kwakawanda kudaro.
Chenjedzo pamusoro pekutsauka (skew)
Mhedzisiro ye straight up iri kure nekugoverwa kwenormal musesheni pfupi: masesheni mazhinji anoramba ari −$10 pakutenderera kwega kwega nekusvetuka kwe+$350 dzimwe nguva. Mutemo we±1σ unotsanangura kupararira zvakarurama asi chimiro zvisina kunaka kusvikira N yasvika mumazana. Pamabheti emubhadharo wakaenzanabhetiBheti remubhadharo wakaenzanaTsvuku/nhema, isina kuenzana/yakaenzana, dzepamusoro/dzepasi. Nhamba 18, rinobhadhara 1:1.Verengai zvese → fungidziro yenormal yakanaka kubva pakutenderera kunenge 30.
Fomula
Mibvunzo
Humbowo hwekuti makatamba masesheni anenge 40, kana kuti makanga muri muiya imwe ine rombo pamakumi mana. Zviitei zvakare.
Inozungunuka zvishoma nezvishoma: standard error yeavhareji i σ/√N. PaN = 10,000 i1% yemari yakabhejwa.
Kutamba neMasvomhu
Edzai izvi imi pachenyu pekutanga. Mhinduro yega yega yakapetwa; ivhurei kana magadzirira.
Pakutenderera 100 kwevhiri reEurope, yunitimariYunitiMari yehwaro inoshandiswa nesisitimu kana nemutambi. Maprogression anotsanangurwa nemayuniti kuitira kuti ashande patafura ipi zvayo.Verengai zvese → imwe patsvukubhetiTsvukuBheti remubhadharo wakaenzana panhamba 18 tsvuku. ChiFrench: rouge.Verengai zvese → iri mberi nekukunda kunenge 51, uye yuniti imwe pastraight upbhetiStraight upNhamba imwe chete, rinobhadhara 35:1.Verengai zvese → iri mberi kana nhamba yayo ikabuda kanenge ka3. Shandisai bell curve kufungidzira mikana yose miviri, mozoienzanisa nemhinduro chaidzo.
Ratidza mhinduro
Mhinduro Tsvuku: bell curve inopa 35.6% uye mhinduro chaiyo i35.5%. Straight up: bell curve inopa 55.0% uye mhinduro chaiyo i50.9%. Nzira pfupi inoshanda patsvuku uye inopotsa panhamba imwe.
Tsvuku: kukunda kune avhareji ye100 × 18/37 = 48.6, nekupararira kwe√(100 × 18/37 × 19/37) = 5.0. Kuva mberi kunoreva 51 kana kupfuura; pakati, 50.5, pari kupararira 0.37 pamusoro peavhareji, uye bell curve inoisa 35.6% pamusoro paipapo. Kuwedzera mikana chaiyo yekukunda 51, 52 … 100 kunopa 35.5%.
Straight up: kubuda kune avhareji ye100/37 = 2.70, nekupararira kwe√(100 × 1/37 × 36/37) = 1.62. Kubuda katatu kana kupfuura kunoreva pamusoro pe2.5, kupararira 0.12 pasi peavhareji: 55.0% nebell curve. Chaizvo, i1 kubvisa mikana yekubuda 0, 1 ne2, 6.5% + 17.9% + 24.7%, izvo zvinosiya 50.9%.
Bell curve inoda mhedzisiro yakawanda kumativi ose eavhareji. Tsvuku inayo mushure mekutenderera 100; nhamba inobuda kasingasviki katatu paavhareji haina. Curve inotopa 8.7% ku“kusabuda”, apo mukana chaiwo uri 6.5%. Taylor (2021) anoisa binomial nebell curve padivi nepadivi nenzira imwe chete iyi.
Kuseka zvishoma
Sesheni imwe pamakumi maviri iri kunze kwetwo sigma. Mumwe munhu anogara ari pamuswe.
Zvinyorwa
- 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.