推 bookticket:感激不盡:) 04/12 22:58
※ 引述《bookticket ()》之銘言：
: 為什麼一般高統課本
: _
: 比較常教 弱大數法則 lim P(|X-μx| <ε)=1,for anyε>0
: n->∞
This version is called the weak law because convergence in probability is
weak convergence of random variables. That is,
_ P
Xn → μx
: _
: 比較少講 強大數法則 lim X=μx
: n->∞
What you worte is wrong
SLLN is as follows:
_ _ a.s.
P(lim Xn =μx ) = 1 or equivalently Xn → μx
n->∞
This version is called the strong law because almost sure convergence is
strong convergence of random variables.
The proof is more complex than that of the weak law and was proved by
A.N. Kolmogorov.
You can see it in this book, "A first course in probability" by S. Ross.
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