作者swinerider (廢人馬)
看板Statistics
標題Re: [問題] 分配收斂與機率收斂
時間Thu Feb 9 23:55:14 2006
※ 引述《htio (htio)》之銘言：
: 2:分配收斂不能implies 機率收斂,可以舉一個簡單,人人看得懂得例子嗎?
X and Y are i.i.d. Bernoulli r.v.'s, P(X=0)=1/2=P(X=1)
Let X_n=Y for n=1,2,...
Obviously X_n converge in distribution to X.
But set ε=1/3, we have P(|X_n-X|>1/3)=1/2>1/3 for all n.
So X_n doesn't converge in probability to X.
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