distribusi binomial (menentukan varian)

2
DISTRIBUSI BINOMIAL Varian Bukti Perhatikan bahwa, i. ii. Misal y=x-2 Varian σ 2 =npq Var ( x ) =E ( x 2 ) (E (x ) 2 ) =E ( x 2 ) ( μx ) 2 ¿ ¿∗) E(x 2 )=E ( x ( x1) + x ) = E ( x ( x1) ) +E ( x ) = E ( x ( x1) )+μx E ( x ( x1 ) ) = x= 0 n x ( x 1 ) ( x n ) p x q nx = x=2 n x ( x1 ) n! x! ( nx ) ! p x q nx = x=2 n ( n2 ) ! ( x 2 ) ! ( n x ) ! n ( n1 ) p 2 p x2 q nx =n ( n 1 ) p 2 x=2 n ( n 2 ) ! ( x 2 ) ! ( n x ) ! p x2 q ( n2) ( x2) =n ( n 1 ) p 2 y=0 n2 ( n 2 ) ! y! ( n x ) ! p y q ( n2 ) y =n ( n 1 ) p 2 ( p + q ) n2 =n ( n 1 ) p 2 ( p + ( 1p ) ) n2 =n ( n 1 ) p 2 ¿ ¿∗)

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DISTRIBUSI BINOMIAL Varian

Bukti

Perhatikan bahwa,i.

ii.

Misal y=x-2

Sehingga