作者eternalism (男子漢 浪漫道)
看板Grad-ProbAsk
標題Re: [商管] [統計] 一題極限機率求解!
時間Thu Jan 28 13:04:14 2010
※ 引述《alex2014 (綠影)》之銘言：
: Let Xn be the sum of the first n outcomes of tossing a six-side die
: repeated in an independent fashion .
: Compute
: lim P( Xn is divisble by 7).
: n->∞
: 感謝統計高手的幫忙!
: 祝學業進步
: 事事順心
令隨機樣本 Xi i=1,2,3,....,n 之 pmf f(Xi)=1/6, Xi=1,2,3,4,5,6
Xbar = Xn / n , By CLT when n→∞, Xbar → N( 7/2, 35/12n )
又依弱大數法則 lim P(|Xbar-7/2|<ε) = 1 , for all ε>0
n→∞
lim Xbar = 7/2 , lim Xn = (7/2)n
n→∞ n→∞
所求 lim P( Xn is divisble by 7) = P(n為偶數) = 0.5
n->∞
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※ 編輯: eternalism 來自: 220.135.207.45 (01/28 13:07)