[理工] [機率]-兩事件發生的 條件期望值
※ [本文轉錄自 Math 看板]
作者: TikalCelts (Σ．﹒‧°★) 看板: Math
標題: [機統] 條件期望值
時間: Sun Aug 30 00:49:41 2009
The number of people enter the elevator on the ground flooris a
Poisson r.v with mean 10. If there are N floors above the fround floor ,
and if each person is equally likely to get off at any one of the N floors,
independently of where the others get off, compute the expected number
of stops that all the elevator will make before discharging all of its
passenger.
my Sol:
let n(t) is the event of Poisson r.v t ~ Uniform (0 - N )
Exp [ P( N(t) | t= Y ] where
P( N(t)| t = Y ) = P( N(t) ,t = Y ) / P( t=Y ) = P( N(t) ,t = Y ) / (1/N)
=> Exp [ P( N(t) ,t = Y ) * N ] = N* Exp [ P( N(t) , t =Y ]
=> 問題在這 我如果一層一層的去分析 這樣可以嗎
如果一層一曾討論 那 λ能算是 10/N 囉! X=1
答案就變成 N [ 1 - λ^x *e^λ/ X! ] |x=1
=> N [1-λ exp^(10/N) ] <-------這樣大家覺得呢????
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