3. Suppose that the number of customers using the consulting service of a statis

Question

3. Suppose that the number of customers using the consulting service of a statistical department follows a Poisson process with a rate of 2 customers per week. a) Given that the service had 2 customers in the first week of the semester, what is the probability that it will have at least one customer in the second week of the semester? (7 pts.) b) What is the probability that it takes exactly four weeks to see two weeks (not necessarily two consecutive weeks) without any customers? (9 pts.) c) What is the probability that the next four weeks see no drought weeks (that is, weeks without any customers)? (9 pts)

Explanation / Answer

here =2

a)here probability for 2nd week does not depend on prior information.

probabilty of at least one customer in second week =P(X>=1)=1-P(X=0)=1-e-t =1-e-2 = 1-0.1353=0.8647

b)probability of no customer in a week=P(X=0) =0.1353

therefore from negative binomial probability it takes 4 week to have 2 week without any customer

=(3C2)*(0.1353)2(1-0.1353)2 =0.0411

c)probability that no drought weeks =P( each week have at least one customer )= (1-0.1353)4 =0.5590

  

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