今晚要考期末考 算到現在~~這題想了好久還是不會 麻煩版上的高手們幫幫忙了 拜託各位了 以下是題目 若是在站上格式不好排的話可以寄到我的信箱 [email protected] 先謝謝大家了 THE SPECIAL CASE OF THE GAMMA DISTRIBUTION IN WHICH α IS A POSITIVE INTERGER n IS CALLED AN ERLANG DISTRIBUTION. IF WE REPLACE β BY 1/λ IN EXPRESSION (4.8), THE ERLANG PDF IS x≧0 f(x;λ,n)=λ(λx)^n-1 e^-λx/(n-1)! (前面的次方只到n-1這邊，e不是次方項，(n-1)!的部分為分母) x＜0 f(x;λ,n)=0 IT CAN BE SHOWN THAT IF THE TIMES BETWEEN SUCCESSIVE EVENTS ARE INDEPENDENT , EACH WITH AN EXPONENTIAL DISTRIBUTION WITH PARAMETER λ, THEN THE TOTAL TIME X THAT ELAPSES BEFORE ALL OF THE NEXT n EVENTS OCCUR HAS PDF f (x;λ,n). a. WHAT IS THE EXPECTED VALUE OF X ? IF THE TIME (IN MINUTES) BETWEEN ARRIVALS OF SUCCESSIVE CUSTOMERS IS EXPONENTIALLY DISTRIBUTED WITH λ= .5 HOW MUCH TIME CAN BE EXPECTED TO ELAPSE BEFORE THE TENTH CUSTOMER ARRIVES? b. IF CUSTOMER INTERARRIVAL TIME IS EXPONENTIALLY DISTRIBUTED WITHλ= .5 , WHAT IS THE PROBABILITY THAT THE TENTH CUSTOMER (AFTER THE ONE WHO HAS JUST ARRIVED) WILL ARRIVE WITHIN THE NEXT 30 MIN? c. THE EVENT｛X≦t｝OCCURS IFF AT LEAST N EVENTS OCCUR IN THE NEXT t UNITS OF TIME. USE THE FACT THAT THE NUMBER OF EVENTS OCCURRING IN AN INTERVAL OF LENGTH t HAS A POISSON DISTRIBUTION WITH PARAMETER λt TO WRITE AN EXPRESSION (INVOLVING POISSON PROBABILITIES) FOR THE ERLANG CDF F(t;λ,n)=p(X≦t). -- http://www.wretch.cc/blog/tensai18 --

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