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 ( x−1) + x ) = E ( x ( x−1) ) +E ( x ) = E ( x ( x−1) )+μx E ( x ( x−1 ) ) = ∑ x= 0 n x ( x −1 ) ( x n ) p x ⋅ q n−x = ∑ x=2 n x ( x− 1 ) n! x! ( n− x ) ! p x ⋅ q n−x = ∑ x=2 n ( n−2 ) ! ( x −2 ) ! ( n −x ) ! n ( n− 1 ) p 2 ⋅ p x− 2 ⋅ q n−x =n ( n −1 ) p 2 ∑ x=2 n ( n −2 ) ! ( x −2 ) ! ( n −x ) ! p x−2 ⋅ q ( n− 2) −( x−2) =n ( n −1 ) p 2 ∑ y=0 n−2 ( n −2 ) ! y! ( n −x ) ! p y ⋅ q ( n−2 ) −y =n ( n −1 ) p 2 ( p + q ) n−2 =n ( n −1 ) p 2 ( p + ( 1−p ) ) n−2 =n ( n −1 ) p 2 ⋅ ¿ ⋅ ¿∗)