1. Suppose at a bank in Boston, they have on average 2.1 customers per minute. a

Question

1. Suppose at a bank in Boston, they have on average 2.1 customers per minute. a) What is the type of random variable used for the number of customers arriving in the next minute? What is the parameter? b) What is the type of random variable used for the number of customers arriving in the next 5 minutes? What is the parameter? c) What is the type of random variable used for the time in-between customers? What is the parameter? d) What is the probability that exactly 6 customers arrive in the next 3 minutes? e) What is the probability that at least 2 customers arrive in the next 2 minutes? f1) What is the probability you must wait more than 1.3 minutes for the next customer to arrive? g) What is the probability you wait more than 2.8 minutes for the next customer given that you have waited more than 1.5 minutes already? h) Compare your previous two answers. Can you explain why they are equal? i) What is the 25th percentile length of wait time for the next customer?

Explanation / Answer

a)
this is poisson distribution with parameter 2.1

b) this is also poisson distribution with parameter 2.1 *5 = 10.5

c)
inter-arrival time follow exponential distribution with parameter 2.1/min

d)
P(X = 6)
in 3 min , X follow poisson distribution with 2.1*3 = 6.3 customer

P(X =6) = e^(-6.3) *6.3^6 / 6! = 0.15946139692

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