Discrete vs Continuous Probability Distributions
Kev sim txheeb cais yog qhov kev sim random uas tuaj yeem rov ua dua tsis muaj sijhawm nrog cov txiaj ntsig paub. Ib qho txawv txav tau hais tias yog qhov sib txawv ntawm qhov sib txawv yog tias nws yog qhov tshwm sim ntawm kev sim ntsuas. Piv txwv li, xav txog kev sim random ntawm flipping ib npib ob zaug; Cov txiaj ntsig tau yog HH, HT, TH, thiab TT. Cia qhov sib txawv X yog tus naj npawb ntawm lub taub hau hauv kev sim. Tom qab ntawd, X tuaj yeem coj qhov tseem ceeb 0, 1 lossis 2, thiab nws yog qhov sib txawv. Saib xyuas tias muaj qhov tshwm sim tseeb rau txhua qhov tshwm sim X=0, X=1, thiab X=2.
Yog li, ib txoj haujlwm tuaj yeem txhais los ntawm cov txheej txheem ua tau mus rau cov lej tiag tiag hauv txoj hauv kev uas ƒ(x)=P(X=x) (qhov tshwm sim ntawm X yog sib npaug rau x) rau txhua qhov ua tau x. Qhov kev ua haujlwm tshwj xeeb no yog hu ua qhov tshwm sim ntawm qhov loj / qhov ntom ntom ntawm qhov sib txawv ntawm qhov sib txawv X. Tam sim no qhov tshwm sim loj ua haujlwm ntawm X, hauv qhov piv txwv no, tuaj yeem sau ua ƒ(0)=0.25, ƒ(1)=0.5, ƒ (2)=0.25.
Tsis tas li, txoj haujlwm hu ua cumulative distribution function (F) tuaj yeem txhais los ntawm cov lej tiag tiag mus rau cov lej tiag tiag li F(x)=P(X ≤x) (qhov tshwm sim ntawm X yog tsawg dua. tshaj lossis sib npaug rau x) rau txhua qhov ua tau x. Tam sim no qhov kev faib ua feem ntawm X, hauv qhov piv txwv no, tuaj yeem sau ua F(a)=0, yog a<0; F(a)=0.25, if 0≤a<1; F(a)=0.75, if 1≤a<2; F(a)=1, if a≥2.
Dab tsi yog qhov kev faib tawm qhov tshwm sim?
Yog tias qhov sib txawv ntawm qhov sib txawv cuam tshuam nrog qhov kev faib tawm qhov tshwm sim yog qhov tsis sib xws, ces qhov kev faib tawm qhov tshwm sim yog hu ua discrete. Xws li ib qho kev faib tawm yog teev los ntawm qhov tshwm sim muaj nuj nqi (ƒ). Cov piv txwv tau muab los saum toj no yog ib qho piv txwv ntawm xws li kev faib tawm vim qhov sib txawv ntawm X tuaj yeem tsuas muaj tus lej tsawg kawg nkaus. Cov piv txwv feem ntau ntawm kev faib tawm qhov tshwm sim tsis sib xws yog kev faib tawm binomial, Poisson faib, Hyper-geometric tis thiab multinomial faib. Raws li pom los ntawm qhov piv txwv, cumulative distribution function (F) yog ib kauj ruam muaj nuj nqi thiab ∑ ƒ(x)=1.
Dab tsi yog qhov kev faib tawm tas mus li?
Yog tias qhov sib txawv tsis sib xws nrog rau qhov muaj feem cuam tshuam kev faib tawm txuas ntxiv, ces qhov kev faib tawm qhov tshwm sim tau hais kom txuas mus ntxiv. Xws li ib qho kev faib tawm yog txhais los ntawm kev faib khoom ua ke (F). Tom qab ntawd nws tau pom tias qhov tshwm sim qhov ntom ntom ua haujlwm ƒ(x)=dF(x) / dx thiab qhov ntawd ∫ƒ(x) dx=1. Kev faib tawm ib txwm, cov tub ntxhais kawm t faib, chi squared faib, thiab F faib yog cov piv txwv zoo sib xws. qhov tshwm sim kev faib tawm.
Dab tsi yog qhov txawv ntawm qhov kev faib tawm qhov tshwm sim tsis sib xws thiab qhov muaj feem cuam tshuam tsis tu ncua?
• Nyob rau hauv discrete probability distributions, random variable txuam nrog nws yog discrete, whereas nyob rau hauv tas li ntawd probability distributions, lub random sib txawv yog tas mus li.
• Nruam qhov muaj feem cuam tshuam feem ntau yog qhia siv qhov muaj peev xwm ua haujlwm ceev, tab sis kev faib tawm qhov tshwm sim tsis sib xws tau qhia siv qhov tshwm sim ntawm qhov ua haujlwm loj.
• Cov phiaj xwm zaus ntawm qhov kev faib tawm qhov tshwm sim tsis tu ncua, tab sis nws txuas ntxiv thaum qhov kev faib tawm tas mus li.
• Qhov tshwm sim uas qhov sib txawv tsis tu ncua yuav xav tias tus nqi tshwj xeeb yog xoom, tab sis nws tsis yog qhov sib txawv ntawm qhov sib txawv ntawm qhov sib txawv.
