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A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 317 ✬ . . . Vzorčno povprečje Oglejmo si vzorčno povprečje, določeno z zvezo X = X1 + · · · + Xn n ki je tudi slučajna spremenljivka. Tedaj je DX = 1 n 2 EX = 1 n = 1 n n Xi, i=1 n EXi = µ i=1 pada z naraˇsčanjem velikosti vzorca, tj. X → µ; (enako nam zagotavlja tudi krepki zakon velikih ˇstevil). ✫ n i=1 DXi = 1 n 2 n i=1 σ 2 = σ2 n Iz druge zveze vidimo, da standardna napaka σX = σ √ n statistike X Univerza v Ljubljani ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
A. Juriˇsić in V. Batagelj: Verjetnostni račun in statistika 318 ✬ ✫ Univerza v Ljubljani ▲ ❙ ▲ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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A. Juriˇsić in V. Batagelj: Verje
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