Bernoulli vs Binomial
Ntau zaus hauv lub neej tiag tiag, peb tuaj hla cov xwm txheej, uas tsuas muaj ob qhov txiaj ntsig tseem ceeb. Piv txwv li, yog tias peb dhau qhov kev xam phaj ua haujlwm uas peb tau ntsib lossis ua tsis tiav qhov kev xam phaj, txawm tias peb lub davhlau tawm raws sijhawm lossis ncua sijhawm. Nyob rau hauv tag nrho cov xwm txheej no, peb tuaj yeem siv lub tswvyim uas yuav tshwm sim 'Bernoulli sim'.
Bernoulli
Ib qho kev sim random nrog tsuas yog ob qhov ua tau nrog qhov tshwm sim p thiab q; qhov twg p+q=1, hu ua Bernoulli kev sim siab rau James Bernoulli (1654-1705). Feem ntau ob qhov txiaj ntsig ntawm kev sim tau hais tias yog 'Success' lossis 'Failure'.
Piv txwv li, yog tias peb xav txog kev pov nyiaj npib, muaj ob qhov txiaj ntsig tau, uas tau hais tias yog 'lub taub hau' lossis 'tail'. Yog peb txaus siab rau lub taub hau poob; Qhov tshwm sim ntawm kev vam meej yog 1/2, uas tuaj yeem txhais tau tias yog P (kev vam meej)=1/2, thiab qhov tshwm sim ntawm kev ua tsis tiav yog 1/2. Ib yam li ntawd, thaum peb dov ob lub dice, yog tias peb tsuas yog txaus siab rau qhov sib npaug ntawm ob lub tsuav yog 8, P (Success)=5/36 thiab P (tsis ua tiav)=1- 5/36=31/36.
Ib txheej txheem Bernoulli yog qhov tshwm sim ntawm qhov kev sim Bernoulli ntawm nws tus kheej; yog li ntawd, qhov tshwm sim ntawm kev vam meej tseem zoo ib yam rau txhua qhov kev sim. Ntxiv rau, rau txhua qhov kev sim ua tsis tiav yog 1-P (kev vam meej).
Vim tias tus neeg taug kev yog kev ywj pheej, qhov tshwm sim ntawm qhov xwm txheej hauv Bernoulli txheej txheem tuaj yeem suav los ntawm kev noj cov khoom ntawm qhov ua tau zoo thiab tsis ua tiav. Piv txwv li, yog tias qhov tshwm sim ntawm kev ua tiav [P(S)] yog qhia los ntawm p thiab qhov tshwm sim ntawm kev ua tsis tiav [P (F)] yog qhia los ntawm q; ces P(SSSF)=p3q and P(FFSS)=p2q2
Bnomial
Bernoulli kev sim ua rau kev faib tawm binomial. Feem ntau ntawm cov sij hawm, tib neeg tau tsis meej pem nrog ob lo lus 'Bernoulli' thiab 'Binomial'. Kev faib tawm Binomial yog suav nrog kev ywj pheej thiab sib npaug ntawm Bernoulli kev sim siab. Binomial faib yog qhia los ntawm lub cim b(k; n, p); b(k;n,p)=C(n,k)pkqn-k, qhov twg C(n,k) is known as binomial coefficient. Lub binomial coefficient C(n, k) tuaj yeem xam los ntawm kev siv cov mis n!/k!(n-k)!.
Piv txwv li, yog tias ib qho kev rho npe tam sim nrog 25% yeej daim pib raug muag ntawm 10 tus neeg, qhov tshwm sim ntawm kev yuav daim pib yeej yog b(1; 10, 0.25)=C(10, 1)(0.25)(0.75)9 ≈ 9 x 0.25 x 0.075 ≈ 0.169
Qhov txawv ntawm Bernoulli thiab Binomial yog dab tsi?
- Bernoulli sim yog ib qho kev sim random nrog tsuas yog ob qhov ua tau.
- Binomial sim yog ib theem ntawm Bernoulli kev sim ua nws tus kheej.
