Tauira o ngā Pātai Kōrero mō te Tohatoha Taurite
Ko te tohatoha ōrite tētahi o ngā momo tohatoha tūponotanga māmā rawa atu i roto i ngā tatauranga. E rua ngā momo matua: te tohatoha ōrite motuhake me te tohatoha ōrite tonu. I roto i tēnei tuhinga, ka matapakihia e mātou ngā momo tohatoha ōrite e rua, ka whakaratohia he tauira, me te matapaki i ngā otinga mō ēnei raruraru.
Tohatoha Kotahi Motuhake
Ko te tohatoha ōrite motuhake he tohatoha tūponotanga e ōrite ana te tūponotanga o ia putanga pea o tētahi whakamātautau, o tētahi huihuinga rānei. Ko ngā tauira māmā ko te huri i tētahi mataono tika, te kōwhiri rānei i tētahi kāri mai i tētahi huinga kāri ōrite.
Tauira Pātai 1
Pātai:
E ono ngā taha o te mataono tika, mai i te 1 ki te 6. Tātaihia te tūponotanga o te whiwhinga o te 4 i te hurihanga kotahi o te mataono.
Kōrero:
Nā te mea he ōrite te tūponotanga o ia taha o te mataono tika kia puta mai, ka taea e tātou te kī ko te tūponotanga o ia taha ko:
P(A) = 1/n
Ko n te tapeke o ngā putanga ka taea. I tēnei wā, ko n = 6.
Nō reira, ko te tūponotanga o te whiwhinga i te nama 4 ko:
P(4) = 1/6 ≈ 0.167, 16.7% rānei
Tauira Pātai 2
Pātai:
Tekau ngā pōro kei roto i tētahi pouaka, he nama mai i te 1 ki te 10. Mēnā ka tangohia matapōkeretia tētahi pōro, kimihia te tūponotanga he nui ake te nama o te pōro i tangohia i te 7.
Kōrero:
Ko te maha o ngā pōro e tika ana ko ngā pōro e 8, e 9, me te 10. Nō reira, e 3 ngā pōro e tika ana i roto i ngā pōro e 10 katoa.
P(B) = te maha o ngā pōro e tutuki ana i ngā tikanga / ngā pōro katoa
P(B) = 3 / 10 = 0.3, 30% rānei
Tohatoha ōrite tonu
Ko te tohatoha ōrite tonu he tohatoha e ōrite ana te tūponotanga o ngā uara katoa i roto i tētahi wā kua whakaritea. He maha ngā wā ka puta tēnei tohatoha i ngā āhuatanga e ōrite ana te tūponotanga o ia putanga i roto i tētahi awhe kua whakaritea.
Tauira Pātai 3
Pātai:
Me kī he taurangi matapōkere a X kua tohatohahia kia ōrite i waenga i te 0 me te 1. Kimihia te tūponotanga kei waenga i te 0.25 me te 0.75 a X.
Kōrero:
Mō te tohatoha ōrite tonu, he pumau te kiato tūponotanga puta noa i te wā katoa. I tēnei wā, ko te wā mai i te 0 ki te 1, ko te tikanga ko te kiato tūponotanga (f(x)) he 1 nā te mea me whai horahanga katoa i raro i te pihi o te tohatoha ōrite o te 1.
Ka taea te tatau i te tūponotanga kei waenganui a X i te 0.25 me te 0.75 hei te horahanga i raro i te kōpiko PDF (Probability Density Function) i waenganui i ēnei rohe e rua.
P(0.25 ≤ X ≤ 0.75) = (b – a) / (d – c)
Ko a me b ngā rohe o raro me o runga o te wā e rapuhia ana e tātou, ā, ko c me d ngā rohe o te tohatoha ōrite. I tēnei wā, ko a = 0.25, b = 0.75, c = 0, me d = 1.
P(0.25 ≤
Nō reira, ko te tūponotanga kei waenga i te 0.25 me te 0.75 a X he 0.5, 50% rānei.
Tauira Pātai 4
Pātai:
Ka mahia he ine mā te whakamahi i tētahi taputapu he rite te tohatoha o te tika puta noa i te wā [2, 5]. Kimihia te tūponotanga ka puta he uara i waenga i te 3 me te 4 mai i te inenga.
Kōrero:
Mō te tohatoha ōrite i te wā [2, 5], he pumau te kiato tūponotanga, ā, ko te horahanga katoa i raro i te pihi ko te 1. Nō reira, ko te kiato tūponotanga (f(x)) ko te 1/(5-2) = 1/3.
Ko te tūponotanga kei waenganui i te 3 me te 4 te inenga ko:
P(3 ≤ X ≤ 4) = (b – a) / (d – c)
Ko a me b ngā rohe o te āputa e rapuhia ana e tātou, ā, ko c me d ngā rohe o te tohatoha ōrite. I tēnei wā, ko a = 3, b = 4, c = 2, me d = 5.
P(3 ≤ X ≤ 4) = (4 – 3) / (5 – 2) = 1/3 ≈ 0.333, 33.3% rānei
Whakamutunga
He taputapu tino whai hua te tohatoha ōrite i roto i te tātari tūponotanga me te tātari tatauranga nā te mea he māmā noa iho, he ngāwari hoki ki te mārama. I roto i ngā āhua motuhake me ngā āhua tonu, ka whakarite te tohatoha ōrite kia ōrite te tūponotanga o ia putanga i roto i tētahi awhe kua hoatu.
Ngā Kaupapa Matua
1. Tohatoha Kotahi Motuhake: He ōrite te tūponotanga o ia putanga i roto i tētahi whānuitanga. Hei tauira: te whiu i tētahi mataono tika.
2. Tohatoha ōrite tonu: He pumau te kiato tūponotanga puta noa i te wā. Hei tauira: te ine i te roa, i te taumaha rānei me te taputapu tika i roto i tētahi awhe.
Mā te mārama ki tēnei ariā, mā roto hoki i ngā tauira me ngā kōrero, ka māmā ake te whakamahi i te tohatoha ōrite ki ngā āhuatanga me ngā rangahau o te ao tūturu. Mā tēnei ka āwhina i te whakamārama i ngā āhuatanga he ōrite ngā putanga pea, ahakoa he āhua motuhake, he āhua tonu rānei.
He whai hua ngā tohatoha ōrite ehara i te mea mō ngā tatauranga anake, engari mō te pūtaiao rorohiko, te miihini, te ōhanga, me te maha atu o ngā mara e hiahiatia ana te whakatau kaupapa, te tātari raraunga rānei. Hei tauira, i roto i ngā whakatauira Monte Carlo, ka whakamahia pinepine ngā tohatoha ōrite hei whakaputa i ngā whārite matapōkere i roto i tētahi awhe motuhake, ka whakamahia hei aromatawai i ngā horopaki me ngā putanga rerekē.
Ko te tumanako kua āwhina tēnei tuhinga i a koe ki te mārama ake ki te tohatoha ōrite me pēhea te whakaoti rapanga. Me mahi tonu kia mōhio ai koe ki tēnei ariā, ā, whakamahia ki ngā take o te ao tūturu e pā ana ki tō mara.
