Fakaofi ʻi he Taimi Lōloa: Ko e Lao ʻo e Ngaahi Fika Lalahi ʻi he Lulēti
Ko e founga ʻoku nofo mālie ai ʻa e ʻavalisi ki he −2.70%, mo e ʻuhinga ʻoku fuoloa ange ai ia ʻi he meʻa ʻoku tau fakakaukau ki ai.
ʻOku ofi atu ʻa e mole ʻavalisi ʻi he vilo ʻe taha ki he −1/37 ʻi he tānaki ʻa e ngaahi vilo, pea ʻoku siʻisiʻi ange hono movetevete ʻo hangē ko e 1/√N. Hili ha vilo ʻe 1,000 ʻi he kulokula, ʻoku angamaheni ke ʻi loto ʻa e ʻavalisi ʻi he ±3% mei hono mahuʻinga ʻamanekina.
Lao ʻo e ngaahi fika lalahi
ʻOku hehema ʻa e ʻavalisi ʻoku lele ʻo e ngaahi peti tauʻatāina ki he mahuʻinga ʻamanekinamatematikaMahuʻinga ʻamanekinaKo e ola ʻavalisi ʻi he peti takitaha ʻi he taimi lōloa. −1/37 ʻo e peti ki he peti ʻIulope angamaheni kotoa pē.Lau kotoa →. Hili ha vilo totongi tatau ʻe N ʻi he iunitipaʻangaIunitiKo e peti tefito ʻoku ngāueʻaki ʻe ha sisitemi pe ha tokotaha vaʻinga. ʻOku fakamatalaʻi ʻa e ngaahi fakalakalaka peti ʻaki ʻa e iuniti koeʻuhi ke ngāue ʻi ha tēpile pē.Lau kotoa → ʻe taha, ko e ʻamanekina ʻo e ola ʻavalisi ʻi he vilo ʻe taha ko e −1/37 pea ko hono mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ko e 1/√N. ʻI he N = 100, ko e movetevete ko iá ko e 10% ia ʻo e peti, ʻo meimei liunga fā ʻo e fakaʻilonga ʻo e 2.7%. ʻI he N = 1,000, ko e 3.2% ia, ʻo meimei tatau mo e fakaʻilonga. ʻI he N = 10,000, ko e 1% ia, pea ʻoku hā mahino ʻa e tuʻunga lelei. ʻOku ʻikai hā ʻa e tuʻunga lelei ʻi ha taimi vaʻinga ʻe taha, ka ʻoku ʻikai lava ke taʻehā ʻi ha taʻu ʻe taha.
Ko e hā ʻoku ofi atu mo e hā ʻoku ʻikai
ʻOku ofi atu ʻa e ʻavalisi ʻi he vilo ʻe taha. ʻOku ʻikai ofi atu ʻa e fakakātoa: ʻoku mamaʻo ange ia mei he noa ʻi he lahi ange ʻa e N, ʻaki ʻa e meimei 2.7% ʻo e N ʻi he ʻamanekina, pea ko hono movetevete takatakai ai ko e √N. Ko ha tokotaha vaʻinga kuo ne vaʻinga ʻi ha vilo ʻe 10,000 ʻi he $10, ʻoku ʻamanekina ke ne mole ʻa e $2,700, ʻo lahi ange pe siʻi ange ʻaki ʻa e $1,000. Kuo fuoloa ʻa e nofo mālie ʻa e konga ʻo e ngaahi kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → ʻi he ofi ki he 48.65%; ka ko e toenga ʻoku lele, ʻoku teʻeki ai ke nofo mālie ia ʻi ha feituʻu.
- p10 −$440
- p25 −$280
- fika lotoloto (median) −$140
- p75 +$0
- p90 +$140
Ko e ʻuhinga ʻoku tō ai ʻa e fakakaukau fakanatula
ʻOku ʻamanekina ʻe he kakai ke hā vave ʻa e tuʻunga lelei koeʻuhí ʻoku ongo lahi ʻa e 2.70%, pea ʻoku nau ʻamanekina ke “tatau” ʻa e ngaahi lele lōloa koeʻuhí ʻoku pehē ʻe he lao ʻo e ngaahi fika lalahimatematikaLao ʻo e ngaahi fika lalahiʻOku ofi ange ʻa e ʻavalisi ʻo e ngaahi ola tauʻatāina ki he mahuʻinga ʻamanekina ʻi he tupu ʻa e lahi ʻo e ngaahi ʻahiʻahi.Lau kotoa → ʻoku ofi atu ʻa e ngaahi ʻavalisi. ʻOku hala ʻa e ongo fakakaukau ko ʻeni ʻi he lahi: ʻoku siʻi ʻa e tuʻunga lelei ʻo fakatatau ki he vēlianimatematikaVēlianiKo ha fua ʻo hono mafola ʻo e ngaahi ola takatakai ʻi he mahuʻinga ʻamanekina. Māʻolunga ki he peti fika ʻe taha, māʻulalo ki he ngaahi peti totongi tatau.Lau kotoa → ʻo ha vilo ʻe taha (σ = iuniti ʻe 1 fakatatau ki he EV = 0.027), ko ia ʻoku fiemaʻu ai ʻa e (1/0.027)² ≈ vilo ʻe 1,400 ke hā ai ʻi he sikima ʻe taha. Pea ʻoku ʻikai toe tohoʻi mai ʻe he ofi atu ʻa e ʻavalisi ʻa e fakakātoa; ʻoku ne fakavaivaiʻi pē ʻa e ngaahi liliu kuo hili.
Ofi atu ki he ngaahi peti kehe
Ki he ngaahi peti fika ʻe tahapetiPeti fika ʻe tahaFika pē ʻe taha, totongi ʻo e 35:1.Lau kotoa →, ko e σ = 5.84, ko ia ʻoku ʻomi ʻe he fika tatau ʻa e (5.84/0.027)² ≈ vilo ʻe 47,000 ke aʻu ʻa e tuʻunga lelei ki he sikima ʻe taha. ʻE lava ha tokotaha vaʻinga peti fika ʻe taha ʻo vaʻinga ʻi ha ngaahi taʻu kae ʻikai lava ke fakamavaheʻi ʻa e tuʻunga lelei mei he monūʻia ʻi hono ngaahi lekooti ʻoʻona, lolotonga ʻoku ne totongi tatau pē ʻa e 2.70% ʻo hangē ko e tokotaha vaʻinga kulokula ʻoku ne sio ki ai ʻi ha ngaahi uike siʻi.
Ko e ʻuhinga ki hono siviʻi ʻo e ngaahi sisitemi
Ko ha taha pē ʻoku ne pehē ʻoku ngāue ha sisitemi, ʻoku totonu ke ne lava ʻo fakahā ia ʻi ha vilo ʻe 10,000 pe lahi ange mo ha ʻavalisi pōsitivi kuo lekooti. ʻI he vilo ʻe 1,000, ko ha ʻavalisi pōsitivi ʻi he totongi tatau ko ha meʻa ia ʻoku hoko taha ʻi he nima ʻi he fakakaukau taʻeʻiai ha meʻa; ʻi he vilo ʻe 100, ʻoku meimei hangē ia ko hono tolo ʻo ha sēniti. ʻOku fakalele ʻe he ngaahi meʻa faʻifaʻitaki ʻi he uepisaiti ni ha taimi vaʻinga ʻe 2,000 ʻo e lōloa ʻoku ke fili ʻi ha sekoni ʻe taha, ʻa ia ko ha fakamoʻoni lahi ange ia ʻi ha fakamoʻoni fakafoʻituitui pē.
Fomula
Ngaahi fehuʻi
ʻOku holo ki he noa ʻa e ngalingalimatematikaNgalingaliKo e faingamālie ʻo ha ola, mei he 0 ki he 1 pe 0% ki he 100%. Fika ʻe taha: 1/37 = 2.70%.Lau kotoa → ke ke toe ʻi muʻa ʻi hoʻo hokohoko atu ʻi he vaʻinga. ʻOku hifo ʻa e fakakātoa ʻo ʻikai ha ngataʻanga.
ʻIkai. ʻOku ʻuhinga ia ʻoku hoko ʻa e ngaahi liliu kuo hili ko ha konga siʻi ange ʻo ha sīpinga lahi ange.
Ki he totongi tatau, ko e meimei 10,000 kimuʻa pea hā mahino ʻa e tuʻunga lelei. Ki he ngaahi peti fika ʻe taha, ko e meimei 50,000.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻOku vaʻinga ʻe ha kaungāmeʻa ʻe toko ua ha takai ʻe 20 ʻo ha vaʻinga faitotonumatematikaVaʻinga faitotonuKo ha vaʻinga ʻoku ʻikai maʻu ʻe ha tafaʻaki ha tuʻunga lelei: ko e peti kotoa pē ʻoku noa hono mahuʻinga ʻamanekina.Lau kotoa →, ko ha lī paʻanga pe ko e kulokulapetiKulokulaPeti totongi tatau ki he fika kulokula ʻe 18. Faka-Falanisē: rouge.Lau kotoa → ʻi he fāitaha mo e ʻuliʻulipetiʻUliʻuliPeti totongi tatau ki he fika ʻuliʻuli ʻe 18. Faka-Falanisē: noir.Lau kotoa → kae fakafoki ʻa e ngaahi noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa →, pea tauhi ha lau hokohoko. Lau ʻa e ngaahi takai ʻoku ʻi muʻa ai ʻa e tokotaha takitaha (ko ha tatau ʻoku lau ia maʻa e tokotaha naʻe ʻi muʻa ʻi muʻa tonu ai). Ko fē ʻoku ngalingali lahi ange: ke vahevahe ʻa e ʻi muʻa ʻi he takai ʻe 10 ki he 10, pe ke ʻi muʻa ha kaungāmeʻa ʻe taha ʻi he 20 kotoa?
Fakahā ʻa e tali
Tali ʻOku ngalingali lahi ange ʻaupito ke ʻi muʻa ha kaungāmeʻa ʻe taha ʻi he takai kotoa ʻe 20: 35.2%, ʻo lau ha taha pē ʻo kinaua, ʻi he fāitaha mo e 6.1% ki ha 10 ki he 10 tatau.
Ko e ngalingali ke tatau ha lau hokohoko faitotonu hili ʻa e takai ʻe 2k ko e u = C(2k, k)/2²ᵏ: 0.246 hili ʻa e takai ʻe 10 pea 0.176 hili ʻa e 20. ʻOku pehē ʻe ha ola mahuʻinga, ko e lao arc-sine, ko e ngalingali ke ʻi muʻa ha kaungāmeʻa kuo fakahingoa ʻi he takai ʻe 2k tofu pē ʻi he 2n ko e u(2k) × u(2n − 2k).
ʻI muʻa ʻi he 20 kotoa: u(20) × u(0) = 0.176 maʻa e kaungāmeʻa takitaha, 35.2% maʻa ha taha pē ʻo kinaua. Ko ha vahevahe tatau: u(10) × u(10) = 0.246² = 6.1%, ko e vahevahe ʻoku siʻi taha hono ngalingali ʻi he kotoa.
Ko ia ʻi ha vaʻinga faitotonu ʻoku tātātaha ke liliu ʻa e tokotaha ʻoku ʻi muʻa. Ko ha tokotaha vaʻinga kuo ʻi muʻa ʻi he efiafi kotoa, pe ʻi mui ʻi he efiafi kotoa, kuo ʻikai ke ne sio ki ha meʻa makehe, pea ʻoku ʻikai ke ne tala ha meʻa ʻo kau ki he veʻeteka pe ki ha poto. ʻOku ʻomi ʻe Epstein (2013) ʻa e lao tatau ki he ngaahi vaʻinga lōloa ange: ʻi he vaeua ʻo e taimi ʻoku ʻi muʻa ʻa e tafaʻaki monūʻia ange ʻi he laka hake ʻi he 85% ʻo e vaʻinga.
Meʻa fakaoli
ʻOku ofi atu ʻa e ʻavalisi. Ko e fakakātoa, ʻoku ʻalu pē ia.
Ngaahi Maʻuʻanga
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.