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A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 309 ✬ Centralni limitni izrek ✫ Vzorčna porazdelitev povprečja Če je naključni vzorec velikosti n izbran iz populacije s končnim povprečjem µ in varianco σ 2 , potem je lahko, če je n dovolj velik, vzorčna porazdelitev povprečja y aproksimirana z gostoto normalne porazdelitve. Naj bo y1, y2, . . . , yn naključni vzorec, ki je sestavljen iz n meritev populacije s končnim povprečjem µ in končnim standardnim odklonom σ. Potem sta povprečje in standardni odklon vzorčne porazdelitve y enaka µ Y = µ, and σ Y = σ √ n . Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 310 ✬ ✫ Hitrost centralne tendence pri CLI Dokaz CLI je precej tehničen, kljub temu pa nam ne da občutka kako velik mora biti n, da se porazdelitev slučajne spremenljivke pribliˇza normalni porazdelitvi. X1 + · · · + Xn Hitrost pribliˇzevanja k normalni porazdelitvi je odvisna od tega kako simetrična je porazdelitev. To lahko potrdimo z eksperimentom: mečemo (ne)poˇsteno kocko, Xk naj bo vrednost, ki jo kocka pokaˇze pri k-tem metu. Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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