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Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two...

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Statistics

Customers arrive in a certain shop according to an approximatePoissonprocess on the average of two every 6 minutes.

(a) Using the Poisson distribution calculate the probability oftwo or more customersarrive in a 2-minute period.

(b) Consider X denote number of customers and X follows binomialdistribution withparametersn= 100. Using the binomial distributioncalculate the probability oftwo or more customers arrive in a2-minute period.

(c) Let Y denote the waiting time in minutes until the firstcustomer arrives. (i) Whatis the pdf ofY? (ii) Findq1=Ï€0.75

(d) Let Y denote the waiting time in minutes until the firstcustomer arrives. What isthe probability that the shopkeeper willhave to wait more than 3 minutes for thearrival of the firstcustomer ?

(e) What is the probability that shopkeeper will wait more than3 minutes before bothof the first two customers arrive?

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