Re: [問題] 有關Poisson分配題目~
※ 引述《kbamj (ya^^)》之銘言：
: 麻煩各位了~有一小題不太了解~
: Calls arriving at a switchboard follow a Poisson process with parameter
: λ=5.2 per minute.
: 1.What is the expected waiting time between the arrivals of two calls?
: 這題我想是把λ=5.2/min轉成θ=23.6sec/2calls,算θ?
interarrival time Ti~iid exp(1/5.2) (單位:mimute)
E[Ti]=1/5.2 (mimute)
: 2.What is the probability that the waiting time between the arrivals of
: two calls is less than 10 seconds?
: 這題就把上題θ,用指數分配,然後積分範圍0~10?
計算 P(Ti<1/6)
: 3.What is the distribution of the time taken for 10 calls to arrive at
: the switchboard?
: 他說10calls時間分配分部?不太了解~
d
題目所求 T = T1+...+T10~Gamma(10,1/5.2)
: 4.What is the expectation of the time taken for 10 calls to arrive at
: the switchboard?
: 10calls期望值?不太了解~
E[T]=10*1/5.2
: 5.What is the probability that less than 5 calls arrive at the switchboard
: during a 1-minute period?
: 這題單純算P(X<5) X=到達calls數 用Poisson?
計算 P(T1+...+T5>1), Ti+...+T5~Gamma(5,1/5.2)
或直接X~Poi(5.2), 計算P(X<5)
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※ 編輯: Jordan23 來自: 140.115.45.112 (04/14 18:31)
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