Laʻana o nā Nīnau Kūkākūkā Hoʻokaʻawale like
ʻO ka hoʻokaʻawale like ʻana kekahi o nā ʻano hoʻokaʻawale like ʻole maʻalahi loa i nā helu helu. Ua māhele ʻia i ʻelua ʻano nui: ka hoʻokaʻawale like ʻole a me ka hoʻokaʻawale like mau. Ma kēia ʻatikala, e kūkākūkā mākou i nā ʻano ʻelua o ka hoʻokaʻawale like ʻana, e hāʻawi i nā laʻana, a e kūkākūkā i nā hoʻonā i kēia mau pilikia.
Hoʻolaha like ʻole
ʻO ka hoʻolaha like ʻole kahi hoʻolaha like ʻole kahi e loaʻa ai i kēlā me kēia hopena hiki o kahi hoʻokolohua a hanana paha kahi manawa like e hiki mai ana. ʻO nā laʻana maʻalahi loa ka ʻōwili ʻana i kahi dice kūpono a i ʻole ke koho ʻana i kahi kāleka mai kahi hoʻonohonoho o nā kāleka like.
Laʻana Nīnau 1
Nīnau:
He 6 ʻaoʻao ko ka make kūpono i helu ʻia mai ka 1 a i ka 6. E hoʻoholo i ka likelika o ka loaʻa ʻana o ka 4 ma ka ʻōwili hoʻokahi o ka make.
Kūkākūkā:
ʻOiai ʻo kēlā me kēia ʻaoʻao o kahi dice kūpono he like ka likelika o ka puka ʻana mai, hiki iā mākou ke ʻōlelo ʻo ka likelika o kēlā me kēia ʻaoʻao:
P(A) = 1/n
ʻO n ka huina o nā hopena hiki. I kēia hihia, ʻo n = 6.
No laila, ʻo ka hiki ke loaʻa ka helu 4 penei:
P(4) = 1/6 ≈ 0.167 a i ʻole 16.7%
Laʻana Nīnau 2
Nīnau:
Aia i loko o kahi pahu he 10 mau pōpō i helu ʻia mai ka 1 a hiki i ka 10. Inā huki ʻia kekahi pōpō ma ke ʻano maʻamau, e ʻimi i ka hiki ke loaʻa i ka pōpō i huki ʻia kahi helu ʻoi aku ma mua o 7.
Kūkākūkā:
ʻO ka helu o nā pōpō kūpono he mau pōpō i helu ʻia he 8, 9, a me 10. No laila, aia he 3 mau pōpō kūpono mai ka huina o 10 mau pōpō.
P(B) = ka helu o nā pōpō e kū ana i nā kūlana / huina pōpō
P(B) = 3 / 10 = 0.3 a i ʻole 30%
Hoʻolaha like mau
ʻO ka hoʻolaha like mau he hoʻolaha ia kahi e loaʻa ai i nā waiwai āpau i loko o kahi wā i hāʻawi ʻia kahi like like o ka hiki ke hana. Hoʻomaka pinepine kēia hoʻolaha i nā kūlana kahi e like like ai ka hopena o kēlā me kēia hopena i loko o kahi laulā i hāʻawi ʻia.
Laʻana Nīnau 3
Nīnau:
Manaʻo ʻia he loli kaulele ʻo X i hoʻokaʻawale like ʻia ma waena o 0 a me 1. E huli i ka hiki ke aia ʻo X ma waena o 0.25 a me 0.75.
Kūkākūkā:
No ka hoʻolaha like mau, ua mau ka nui o ka hiki ke hoʻololi ʻia ma ka wā holoʻokoʻa. I kēia hihia, ʻo ka wā mai 0 a 1, ʻo ia hoʻi ka nui o ka hiki ke hoʻololi ʻia (f(x)) he 1 no ka mea, pono i kahi hoʻolaha like ke loaʻa kahi ʻāpana holoʻokoʻa ma lalo o ke kūlou o 1.
Hiki ke helu ʻia ka likelika o X ma waena o 0.25 a me 0.75 ma ke ʻano he wahi ma lalo o ka piʻo PDF (Probability Density Function) ma waena o kēia mau palena ʻelua.
P(0.25 ≤ X ≤ 0.75) = (b – a) / (d – c)
ʻO a a me b nā palena haʻahaʻa a me luna o ka wā a mākou e ʻimi nei, a ʻo c a me d nā palena o ka hoʻolaha like. I kēia hihia, ʻo a = 0.25, b = 0.75, c = 0, a me d = 1.
P(0.25 ≤
No laila, ʻo ka likelika e noho ana ʻo X ma waena o 0.25 a me 0.75 he 0.5 a i ʻole 50%.
Laʻana Nīnau 4
Nīnau:
Hana ʻia kahi ana me kahi mea hana me kahi hoʻolaha like o ka pololei ma luna o ka wā [2, 5]. E ʻimi i ka hiki ke loaʻa i ke ana kahi waiwai ma waena o 3 a me 4.
Kūkākūkā:
No ka hoʻolaha like ʻana ma ka wā [2, 5], ua paʻa ka nui o ka hiki ke hoʻololi a ʻo ka huina o ka ʻāpana ma lalo o ke kūlou he 1. No laila, ʻo ka nui o ka hiki ke hoʻololi (f(x)) he 1/(5-2) = 1/3.
ʻO ka hiki ke ana ʻia ma waena o 3 a me 4 penei:
P(3 ≤ X ≤ 4) = (b – a) / (d – c)
ʻO a a me b nā palena o ka wā a mākou e ʻimi nei, a ʻo c a me d nā palena o ka hoʻolaha like. I kēia hihia, ʻo a = 3, b = 4, c = 2, a me d = 5.
P(3 ≤ X ≤ 4) = (4 – 3) / (5 – 2) = 1/3 ≈ 0.333 a i ʻole 33.3%
Ka hopena
He mea hana pono loa ka hoʻolaha like ʻana i ka hiki ke loaʻa a me ka loiloi helu ma muli o kona maʻalahi a me ka maʻalahi o ka hoʻomaopopo ʻana. Ma nā ʻano discrete a me nā ʻano hoʻomau, hōʻoia ka hoʻolaha like ʻana e loaʻa i kēlā me kēia hopena i loko o kahi pae i hāʻawi ʻia ka like o ka hiki ke loaʻa.
Nā Manaʻo Koʻikoʻi
1. Ka Hoʻolaha like ʻole: ʻO ka likelika o kēlā me kēia hopena i loko o kahi laulā i manaʻo ʻia he like. Laʻana: ke kiola ʻana i kahi dice kūpono.
2. Hoʻolaha like mau: Kūpaʻa ka nui o ka hiki ke hoʻololi i loko o ka wā. Laʻana: ke ana ʻana i ka lōʻihi a i ʻole ke kaumaha me kahi mea hana pololei i loko o kahi laulā.
Ma ka hoʻomaopopo ʻana i kēia manaʻo a ma o nā laʻana a me nā kūkākūkā ʻana, hiki iā mākou ke hoʻopili maʻalahi i ka hoʻolaha like ʻana i nā kūlana like ʻole o ka honua maoli a me ka noiʻi. Kōkua kēia i ka wehewehe ʻana i nā hanana i loaʻa nā hopena like, inā paha ma ke ʻano ʻokoʻa a hoʻomau paha.
He mea pono nā hoʻolaha like ʻole ʻaʻole wale ma nā helu helu, akā, ma ka ʻepekema kamepiula, ka ʻenekinia, ka hoʻokele waiwai, a me nā ʻoihana ʻē aʻe he nui kahi e pono ai ka hoʻoholo ʻana a i ʻole ka nānā ʻana i ka ʻikepili. No ka laʻana, ma nā simulations Monte Carlo, hoʻohana pinepine ʻia nā hoʻolaha like e hana i nā vectors random i loko o kahi laulā kikoʻī, a laila hoʻohana ʻia e loiloi i nā hiʻohiʻona like ʻole a me nā hopena.
Lana ko mākou manaʻo ua kōkua kēia ʻatikala iā ʻoe e hoʻomaopopo maikaʻi i ka hoʻolaha like ʻana a pehea e hoʻoponopono ai i nā pilikia me ia. E hoʻomau i ka hoʻomaʻamaʻa ʻana e hoʻopaʻa i kēia manaʻo a hoʻopili iā ia i nā hihia maoli e pili ana i kāu kahua.
