Question

Question 5: In a retail store, the number of transactions in which the customer pays with a credit card is well modelled by a Poisson process with a rate of 3 per hour.

a) Calculate the probability that between 4 and 8 credit card transactions are made in a 2-hour period.

b) What is the probability that the waiting time between credit card transactions is between 30 mins and 45 mins?

Answer 1

Let X denotes the credit card transactions are made in a 2-hour period.

X ~ Poisson(3*2) or X ~ Poisson(6)

The probability mass function of X is

Now,

The probability that between 4 and 8 credit card transactions are made in a 2-hour period

b) Let Y denotes the waiting time between credit card transactions.

Y follows Exponential distribution with mean = 60/3 = 20

Now,

The probability that the waiting time between credit card transactions is between 30 mins and 45 mins