Xt n xt
Ｍ (t) = Ｅ(ｅ ) = Σ e ．f(x)
x x=0
n xt n x n-x
= Σ e ．Ｃ ．p ．(1-p)
x=0 x
n n t x n-x
= Σ Ｃ ．(pｅ) ．(1-p)
x=0 x
t n
= [ pe + (1-p) ]
t n
=(pe + q)
1 │
1 d │
Ｅ(X) = Ｍ = ── Ｍ (t)│
0 1 x │
dt │t=0
1 │
d t n│
= ── (pe + q) │
1 │
dt │t=0
│
t n-1 t│
= n．(pe + q) ．pe │
│
│t=0
n-1
= n．(p + q) ．p = n．p
2 │ 1 │
2 2 d │ d t n-1 t │
Ｅ(X ) = Ｍ = ── Ｍ (t)│ = ── [n．(pe + q) ．pe ]│
0 2 x │ 1 │
dt │t=0 dt │t=0
│
t n-2 t t t n-1 t│
= n．(n - 1)．(pe + q) ．pe ．pe + n．(pe + q) ．pe │
│
│t=0
n-2 n-1
= n．(n-1)．(p + q) ．p．p + n．(p + q) ．p
2
= n．(n-1)．p + n．p
2 2 2
= n ．p - n．p + n．p
2 2
Var(X) = Ｅ(X ) - [Ｅ(X)]
2 2 2 2
= (n ．p - n．p + n．p) - (n．p)
2
= n．p - n．p
= n．p．(1-p)
= n．p．q
※ 编辑: ji3g4al6al6 来自: 122.121.80.252 (08/23 23:03)