作者linwish (請多指教)
看板Statistics
標題[問題] martingale
時間Wed Nov 12 15:15:27 2008
1.let (ξ_n) be a sequence of iid Bernoulli random variables with generating
n
function M(t)=E[exp(tξ_1)]<∞ fot t≠0 and let X_n=Σξ_i
i=1
prove that the sequence (Z_n) with Z_n=exp(tX_n)/M^n(t) is a martingale.
2.let X and Y be integrable random variables on a probability space (Ω,F,P)
then we can decompose Y into Y=Y_1+Y_2
where Y_1=E[Y∣X] and Y_2=Y-E[X∣Y]
(a) show that Y_2 and X are uncorrelated.
(b)More general, show that Y_2 is uncorrelated with every σ(X)-measurable
random variable.
想了很久解不出來的問題這此請教大家了 感謝
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1F：推 casella123:請由定義下手，試試看囉！ 11/12 16:17
2F：→ linwish:抱歉 小的就是走定義走不不出來才來發問的 11/13 00:50
3F：推 clickhere:1. \xi~B(p), X_n~B(n,p),by martingale定義證. 11/13 03:25
4F：推 clickhere:2(a). Y_1=E[Y|X]=E[X|Y]=c,Y_2=Y-c indep. of X? 11/13 03:29
5F：推 casella123:試著把算是寫出來 在幫你看看卡在哪裡 11/13 09:28