Re: [問題] sample variance
※ 引述《moon2519 (~X~X~)》之銘言：
: 給定 X(i) (for i=1,2.3,...,n)為一random sample
: S^2 為其樣本變異數
: 考慮 E[X(i)] = theta1
: E[X(i)-theta1]^2 = theta2
: E[X(i)-theta1]^3 = theta3
: E[X(i)-theta1]^4 = theta4
: Show that Var(S^2) = [theta4 - (n-3)*(theta2)^2/(n-1)]/n
Σ(Xi-X.bar)^2 Σ(Xi-theta1+ theta1-X.bar)^2
S^2 = ----------------- = ------------------------------
n - 1 n-1
Σ(Xi-theta1)^2 - n(theta1-X.bar)^2
= ------------------------------------ (X.bar = ΣXi/n)
n-1
Σ(Xi-theta1)^2 - Σ(theta1-X.bar)^2 /n
= -----------------------------------------
n-1
Var(S^2)=E(S^4)-[ES^2]^2 = E(S^4) - theta2
ES^4 就小心展開計算一下..應該就會得到你要的結果了...答案有了就湊一下吧..
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