Te Hipanga Paerewa i te Rūreti
Ko te hipanga paerewa o te rūreti, te pūtake rua o te tītaringapāngarauTītaringaHe inenga o te whānui o te marara o ngā hua huri noa i te uara tūmanako. He teitei mō te tau kotahi, he hakahaka mō ngā peti utu ōrite.Pānuitia katoatia →, te tawhiti auau i waenga i tētahi hua me tōna tūmanako.
Mō ia $1 ka petihia, ko te σ he 5.84 mō te tau kotahi, he 1.00 mō te whero. Whakareatia ki te moni peti me te pūtake rua o te maha o ngā hurihanga mō tētahi wā tākaro.
Ture māmā
Tata ki te rua hautoru o ngā wā tākaro ka tau ki roto i te σ kotahi o te tūmanako, ā, ko te 95% ki roto i te rua. Mō ngā hurihanga wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → 100 i te $10 (tūmanako −$27, σ = $100) ko te nuinga o ngā wā tākaro ka taka ki waenga i te −$127 me te +$73, ā, tata ki te katoa ki waenga i te −$227 me te +$173. Ko te hua i waho o taua awhe ehara i te taunakitanga o tētahi mea, hāunga anake kotahi i roto i ngā wā tākaro e rua tekau ka pērā.
He aha te √N
Ka tupu te ngaronga tūmanakopāngarauNgaronga tūmanakoTe uara tūmanako whakareatia ki te tapeke o te moni kua petihia; te moni toharite ka ngaro i roto i te wā tākaro, i tētahi wā rānei.Pānuitia katoatia → e ai ki te N; ka tupu te horahanga e ai ki te √N. Mō te N iti ka nui ake te horahanga, ā, he rite ngā wā tākaro ki te maka moni me te paku tītaha. Mō te N nui ka hipa te ngaronga i te horahanga. Ko te pae whakawhiti, ina ōrite te ngaronga tūmanako ki te hipanga paerewapāngarauHipanga paerewaTe pūtake rua o te tītaringa; te tawhiti noa o te hua i te uara tūmanako.Pānuitia katoatia → kotahi, kei te N = (σ/painga)² = (1/0.027)² ≈ 1,370 hurihanga mō te utu ōrite, ā, kei te (5.84/0.027)² ≈ 46,800 mō ngā tau kotahipetiTau kotahiHe tau kotahi, ko te utunga 35:1.Pānuitia katoatia →. Ki raro iho i aua tatau, mā te waimarie e whakatau; ki runga ake, mā te painga.
Te whakamahi
Hei whakatau mēnā he rerekē tētahi wā tākaro, tātaihia te (hua − EV)/σ. Ko te kaipeti whero $10 ka mutu i ngā hurihanga 100 i te +$150, kei te (150 + 27)/100 = 1.77σ, he putanga kotahi i roto i te 25: he waimarie, ehara i te mea mīharo. Ko te kaipeti tau kotahi i taua +$150 anō, kei te 0.3σ: he pō noa. He rerekē te tikanga o taua hua ā-tāra anō i ngā peti rerekē.
Te hapa paerewa o tētahi ōwehenga
Mā taua tātai anō e kī mai e hia ngā hurihanga e kitea ai te painga i ngā raraunga. Ko te hapa paerewa o tētahi ōwehenga toa kua kitea he √(p(1 − p)/N). Mō te whero me te N = 1,000: √(0.4865 × 0.5135 / 1000) ≈ 1.6%. Ko te āputa i waenga i te moni maka tōkeke me te whero he 1.35%, nō reira i muri i ngā hurihanga 1,000 kāore tonu e taea e koe te wehewehe mārika. I muri i ngā hurihanga 10,000 ko te hapa paerewa he 0.5%, ā, ka taea e koe. Koinā hoki te take e hiahiatia ai ngā hurihanga maha hei kite i te wīra tītaha.
He whakatūpato mō te tītaha
Ko ngā hua tau kotahi i tētahi wā tākaro poto kāore rawa i te tohatoha noa: ko te nuinga o ngā wā tākaro he −$10 tonu i ia hurihanga me ētahi pekenga +$350 i ētahi wā. Ka tika te whakaahua a te ture ±1σ i te horahanga, engari he hē te āhua tae noa ki te wā kei ngā rau te N. Mō ngā peti utu ōritepetiPeti utu ōriteWhero/pango, kehe/taurite, teitei/hakahaka. 18 ngā tau, ko te utunga 1:1.Pānuitia katoatia → he pai te tatau tata noa mai i ngā hurihanga 30 pea.
Tātai
Ngā pātai
He taunakitanga i tākaro koe tata ki ngā wā tākaro 40, i a koe rānei te mea waimarie kotahi i roto i te whā tekau. Mahia anō.
Ka iti haere te piu: ko te hapa paerewa o te toharite he σ/√N. Ā te N = 10,000 he 1% o te moni peti.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
I ngā hurihanga 100 o te wīra Ūropi, kei mua te waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia → kotahi ki te wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → mēnā e 51 ngā toa, nui ake rānei, ā, kei mua te wae kotahi ki te tau kotahipetiTau kotahiHe tau kotahi, ko te utunga 35:1.Pānuitia katoatia → mēnā ka pā tōna tau kia 3 ngā wā, nui ake rānei. Whakamahia te ānau pere hei whakatau tata i ngā tūpono e rua, kātahi ka whakatairite ki ngā whakautu tika.
Whakaaturia te otinga
Whakautu Whero: ka hoatu e te ānau pere te 35.6%, ā, ko te whakautu tika ko te 35.5%. Te tau kotahi: ka hoatu e te ānau pere te 55.0%, ā, ko te whakautu tika ko te 50.9%. Ka whai hua te ara poto mō te whero, ā, ka hapa mō te tau kotahi.
Whero: ko te toharite o ngā toa ko te 100 × 18/37 = 48.6, me te horanga o te √(100 × 18/37 × 19/37) = 5.0. Ko te noho ki mua ko te 51, nui ake rānei; ko te tohu haurua, 50.5, he 0.37 horanga ki runga ake i te toharite, ā, ka whakatau te ānau pere i te 35.6% ki runga ake i tērā. Mā te tāpiri i ngā tūpono tika o ngā toa 51, 52 … 100 ka puta te 35.5%.
Tau kotahi: ko te toharite o ngā pānga ko te 100/37 = 2.70, me te horanga o te √(100 × 1/37 × 36/37) = 1.62. Ko ngā pānga e toru, nui ake rānei, ko te nui ake i te 2.5, 0.12 horanga ki raro iho i te toharite: 55.0% mā te ānau pere. Mā te tika, ko te 1 tango i ngā tūpono o ngā pānga 0, 1 me te 2, 6.5% + 17.9% + 24.7%, ka toe ko te 50.9%.
Me maha ngā hua o te ānau pere i ngā taha e rua o te toharite. Kei te whero ēnā i muri i ngā hurihanga 100; kāore i te tau ka pā iti iho i te toru wā i te toharite. Ka hoatu anō e te ānau te 8.7% ki te “kāore he pānga”, ko te tūpono pono ko te 6.5%. Ka whakatakotoria e Taylor (2021) te tohatoha huarua me te ānau pere taha ki te taha i taua āhua anō.
He katakata iti
Kotahi i roto i ngā wā tākaro e rua tekau kei waho i te rua sigma. Kei te hiku tonu tētahi.
Ngā Puna
- 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.