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Fri Feb 10 13:40:44 2006
※ 引述《swinerider (廢人馬)》之銘言：
: 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.
Convergence in probability means that given ε>0 there is an N s.t.
P(|X_n-X|>ε)<ε for all n>=N (*).
In the example above, (*) does not hold.
P.S. (*)是許多等價敘述中的其中一種, 例如可以改用:
Given ε>0,δ>0 there is an N s.t. P(|X_n-X|>ε)<δ for all n>=N.
不過都是等價的.
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