Video: Chebyshev qhov tsis sib xws hais li cas?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Chebyshev qhov tsis sib xws hais tias uas tsawg kawg yog 1-1 / K2 ntawm cov ntaub ntawv los ntawm tus qauv yuav tsum poob hauv K tus qauv sib txawv ntawm qhov nruab nrab (ntawm no K yog ib tus lej tiag tiag ntau dua ib qho). Tab sis yog cov ntaub ntawv teev yog tsis muab faib rau hauv cov duab ntawm lub tswb nkhaus, ces tus nqi sib txawv tuaj yeem nyob hauv ib qho qauv sib txawv.
Raws li txoj cai, Chebyshev qhov tsis sib xws ntsuas yog dab tsi?
Chebyshev qhov tsis sib xws (tseem hu ua Tchebysheff's kev tsis sib xws ) yog a ntsuas ntawm qhov kev ncua deb ntawm qhov nruab nrab ntawm ib qho random cov ntaub ntawv taw tes hauv ib txheej, qhia raws li qhov tshwm sim. Nws hais tias rau cov ntaub ntawv teeb tsa nrog qhov sib txawv tsis tu ncua, qhov tshwm sim ntawm cov ntaub ntawv taw qhia nyob hauv k tus qauv sib txawv ntawm qhov nruab nrab yog 1 / k2.
Tsis tas li ntawd, Chebyshev's theorem formula yog dab tsi? Chebyshev's theorem xeev rau ib qho k> 1, tsawg kawg yog 1-1 / k2 ntawm cov ntaub ntawv nyob rau hauv k standard deviations ntawm qhov nruab nrab. Raws li tau hais, tus nqi ntawm k yuav tsum ntau dua 1. Siv qhov no qauv thiab ntsaws rau hauv tus nqi 2, peb tau txais txiaj ntsig ntawm 1-1/22, uas yog sib npaug li 75%.
Khaws qhov no hauv kev xav, koj ua pov thawj Chebyshev qhov tsis sib xws li cas?
Ib txoj kev los ua pov thawj Chebyshev qhov tsis sib xws yog siv Markov's kev tsis sib xws mus rau random variable Y = (X − Μ)2 nrog a = (kσ)2. Chebyshev qhov tsis sib xws ces ua raws li kev faib los ntawm k2σ2.
Chebyshev's theorem yog dab tsi thiab nws siv li cas?
Chebyshev's theorem yog siv txhawm rau nrhiav qhov kev faib ua feem ntawm kev soj ntsuam koj xav kom pom nyob rau hauv ob qho kev sib txawv ntawm qhov nruab nrab. Chebyshev cov Interval yog hais txog cov ntu uas koj xav pom thaum siv lub theorem . Piv txwv li, koj lub sijhawm yuav yog los ntawm -2 mus rau 2 tus qauv sib txawv ntawm qhov nruab nrab.
Pom zoo:
Vim li cas peb thiaj li hais txog kev txwv tsis pub muaj kev hais tawm thiab thaum twg peb yuav hais cov kev txwv?
Peb hais txog kev txwv vim nws yuav ua rau qhov sib npaug tsis tau txhais hauv qee qhov txiaj ntsig ntawm x. Qhov kev txwv ntau tshaj plaws rau cov lus qhia muaj nuj nqis yog N / 0. Qhov no txhais tau tias txhua tus lej muab faib los ntawm xoom tsis tau txhais. Piv txwv li, rau txoj haujlwm f(x) = 6/x², thaum koj hloov x = 0, nws yuav ua rau 6/0 uas tsis tau txhais
Puas yog ob txoj kab sib luag zoo sib xws lossis tsis sib xws?
Yog tias ob qhov sib npaug piav txog kab sib luag, thiab yog li cov kab uas tsis sib tshuam, qhov system yog ywj siab thiab tsis sib haum. Yog hais tias ob qhov sib npaug piav txog tib kab, thiab yog li cov kab uas hla tus lej tsis kawg, lub kaw lus yog nyob ntawm thiab sib xws
Koj yuav ua li cas thiaj daws tau qhov sib npaug ntawm qhov tsis sib xws?
Muaj peb kauj ruam: Rov kho qhov sib npaug kom 'y' nyob rau sab laug thiab txhua yam ntawm sab xis. Teem lub 'y =' kab (ua rau nws yog ib txoj kab ruaj khov rau y≤ lossis y≥, thiab ib txoj kab dashed rau y) Duab ntxoov ntxoo saum kab rau 'ntau tshaj' (y> lossis y≥) lossis hauv qab kab rau ib qho 'tsawg dua' (y < lossis y≤)
Vim li cas koj tig lub cim tsis sib xws thaum koj sib npaug lossis faib los ntawm qhov tsis zoo?
Thaum koj muab ob sab los ntawm tus nqi tsis zoo koj ua rau sab uas ntau dua muaj 'loj' tus lej tsis zoo, uas txhais tau tias tam sim no tsawg dua lwm sab! Qhov no yog vim li cas koj yuav tsum tig lub cim thaum twg koj muab los ntawm tus lej tsis zoo
Koj yuav daws qhov kev sib npaug lossis qhov tsis sib xws li cas?
Txhawm rau daws qhov tsis sib xws siv cov kauj ruam hauv qab no: Kauj Ruam 1 Tshem tawm cov feem ntau los ntawm kev muab tag nrho cov ntsiab lus los ntawm tus lej qis tshaj ntawm txhua feem. Kauj Ruam 2 Ua kom yooj yim los ntawm kev sib txuas zoo li cov ntsiab lus ntawm txhua sab ntawm qhov tsis sib xws. Kauj Ruam 3 Ntxiv lossis rho tawm kom tau txais qhov tsis paub ntawm ib sab thiab tus lej ntawm lwm qhov