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A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 325 ✬ Porazdelitvena funkcija za χ 2 je Fχ2 = P (χ 2 Z Z < z) = ✫ . . . Vzorčna disperzija Z . . . P ni=1 y 2 i − 1 n (P n i=1 y i) 2
A. Juriˇ<strong>si</strong>ć in V. Batagelj: Verjetnostni račun in statistika 326 ✬ ✫ . . . Vzorčna disperzija Kakˇsna pa je ta porazdelitev? Ker so tudi kvadrati Z 2 1, Z 2 2, . . . ,Z 2 n−1 med seboj neodvisni in porazdeljeni po zakonu χ 2 (1), je njihova vsota porazdeljena po zakonu χ 2 (n − 1). Tako je torej porazdeljena tudi statistika χ 2 . Ker vemo, da je Eχ 2 (n) = n in Dχ 2 (n) = 2n, lahko takoj izračunamo in ES 2 0 = E σ2 χ 2 n DS 2 0 = D σ2 χ 2 n = (n − 1)σ2 n = 2(n − 1)σ4 n 2 ES 2 = E σ2 χ 2 n − 1 DS 2 = D σ2 χ 2 n − 1 Univerza v Ljubljani ▲ ❙ ▲ ▲ = σ2 = 2σ4 n − 1 ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
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✬ ✫ Ljubljana, 6. oktober 2008
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A. Juriˇsić in V. Batagelj: Verje
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