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?
