作者xu3jp68 (信箱爆炸..XD)
看板Statistics
標題Re: [問題] Definition the poisson process
時間Sun May 21 20:02:48 2006
※ 引述《[email protected] (老怪物)》之銘言：
: ※ 引述《[email protected] (信箱爆炸..XD)》之銘言：
: > The number of in any interval of length t is poisson distribution with
: > mean λt That is for all s,t≧0
: > (λt)^n
: > P{N(t+s)-N(s)=n}=(e^-λt) ----------
: > n!
: > 該如何利用這個證明
: > P(N(h)=1)=λh+o(h)
: N(0)=0 with probability 1
: P[N(h)=1] = P[N(h)-N(0)=1] = (λh)e^{-λh}
不過為什麼課本會寫成λh+o(h)會跟(λh)e^{-λh}相等嗎??
: > P(N(h)≧2)=o(h) o(h):big o function
: P[N(h)≧2] = 1 - P[N(h)=0] - P[N(h)=1]
: = 1 - (1+λh)e^{-λh}
: > 出處:Probability model eighth edition by Ross P289.290
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