The arrival times of customers at a sandwich shop occur at a

The arrival times of customers at a sandwich shop occur at average rate of 1 every 5 minutes. Let C represent the number of customers arriving between 1:30 pm and 1:45 pm.

a. Distribution?

b. Parameter(s)?

c. Support?

Solution

Number of customers arrived is Poisson random variable with

parameter lambda = 3*1 = 3 per 15 minute

and support = (0,1,2,3...)

(support is set of points all those points which have positive probability)