作者starsky822 (豆漿)
看板Math
標題[機統] 指數型分配問題
時間Tue Nov 27 22:28:00 2012
各位大大好~
有2題問題不太懂因此尋求各位的幫忙
問題1
The service times at teller windows in a bank were found to follow an
exponential distribution with a mean of 3.4 minutes. A customer arrives at a
window at 4:00 p.m.
a) Find the probability that he will still be there at 4:02 p.m.
b) Find the probability that he will still be there at 4:04 p.m. given that he
was there at 4:02 p.m.
問題2
Let X be an exponential random variable with mean θ. Show that
E(X k =>k為上標 ) = k!θk=>後面k為上標 Hint: Make use of the gamma function.
此題我的方法是像求E(X^2)，但道一半就亂掉了@@
求祥解
以上先謝謝大家!!!
感謝!
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推 KAINTS :你第一題問題是? 11/27 22:59
→ KAINTS :第二題令x/⊙=u(手機打不出來代替一下),就可以解了 11/27 23:02
→ starsky822 :不知 從何動手@@" 11/27 23:30
推 KAINTS :幾點到就當0阿，第二題用無記憶觀念解 11/27 23:32
推 goshfju :2.就積分硬幹阿 11/28 02:38
→ goshfju : E(X^k)=∫x^k*1/θ*e^(-x/θ)dx 11/28 02:39
→ goshfju : =(1/θ)∫x^(k+1-1)*e^(-x/θ)dx 11/28 02:40
→ goshfju : =(1/θ)*Γ(k+1)*θ^(k+1) 11/28 02:41
→ goshfju : =k!*θ^k 11/28 02:41
→ KAINTS :推文中第四行指的都是問題1喔 11/28 09:01
→ starsky822 :ok!感謝K大和g大，謝謝!!! 11/28 11:05