Iyini i-central limit theorem
Context:Emcabangweni wokunokwenzeka, i-central limit theorem (i-CLT) isungula ukuthi, ezimweni eziningi, kumasampula azimele asatshalaliswe ngokufana, isampula elilinganisiwe lisho ukusatshalaliswa okujwayelekile okujwayelekile noma ngabe izinto eziguquguqukayo zangempela ngokwazo azisatshalaliswa ngokujwayelekile.  I-theorem ingumqondo oyisihluthulelo emcabangweni wokunokwenzeka ngoba kusho ukuthi izindlela zokunokwenzeka nezibalo ezisebenza ngokusatshalaliswa okujwayelekile zingasetshenziswa ezinkingeni eziningi ezibandakanya ezinye izinhlobo zokusatshalaliswa.  Le theorem iye yaba nezinguquko eziningi phakathi nokuthuthukiswa okusemthethweni kwethiyori yamathuba. Izinguqulo zangaphambilini zale theorem zaqala ngo-1811, kodwa ngendlela yayo yesimanje, lo mphumela oyisisekelo emfundisweni yokungenzeka kwathiwa ngokunembile ngasekupheleni kuka-1920, ngaleyo ndlela wakhonza njengebhuloho phakathi kwethiyori yokungenzeka kwe-classical neyesimanje.
Ngokwesibonelo, ake sithi kutholakala isampula eliqukethe ukubonwa okuningi, ukubonwa ngakunye okwenziwa ngokungahleliwe ngendlela engahambisani namanani okunye ukubonwa, nokuthi isilinganiso sezibalo samagugu abonwe siyabalwa. Uma le nqubo yenziwa izikhathi eziningi, i-central limit theorem ithi ukusatshalaliswa kokungenzeka kwesilinganiso kuzosondela kakhulu ekusatshalalisweni okujwayelekile.  I-central limit theorem inezinhlobo eziningana. Ngendlela evamile, izinto eziguquguqukayo ezingahleliwe kufanele zizimele futhi zisatshalaliswe ngendlela efanayo (i.i.d.). Ezinguqulweni, ukuguquguquka kwesilinganiso kuya ekwabelweni okujwayelekile kwenzeka futhi ekwabelweni okungafani noma ekubukeni okungazimele, uma kuhambisana nemibandela ethile.  Inguqulo yokuqala yale theorem, ukuthi ukusatshalaliswa okujwayelekile kungasetshenziswa njengokulinganisa ukusatshalaliswa kwe-binomial, yi-de Moivre <unk> Laplace theorem.