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distribusi normal (menentukan varian (mgf))

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DISTRIBUSI NORMAL Var(x) = M x ’’(t) – (M x ’(t)) 2 = ( e μt+ σ 2 t 2 2 ( μ 2 + 2 μσ 2 t +σ 4 t 2 +σ 2 )) - ( e μt+ σ 2 t 2 2 ( μ +σ 2 . t )) 2 = ( e μt+ σ 2 t 2 2 ( μ 2 + 2 μσ 2 t +σ 4 t 2 +σ 2 )) - ( e 2 μt+ σ 2 t 2 ( μ 2 +2 μσ 2 t+σ 4 t 2 )) = e μt + σ 2 t 2 2 ( μ 2 +2 μσ 2 t+σ 4 t 2 +σ 2 - μ 2 −2 μσ 2 t−σ 4 t 2 = e μt + σ 2 t 2 2 ( σ 2 )|t=0 = e 0+ 0 2 ( σ 2 ) = 1. ( σ 2 ) = σ 2

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DISTRIBUSI NORMALVar(x) = Mx(t) (Mx(t))2

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