# Cofee shop customers

1. Aug 8, 2004

### cosmonova

I've been working on this problem for quite a long time now but I'm not being able to solve it. It goes as follows :

A coffee shop opens his doors from 9.00 to 1.pm.
supposedly 8 customers will enter this shop and stay for a period of half an hour.
Let X be the number of customers present in this shop at a certain time t, what is the probabilty mass function of X ?

Thank you.

2. Aug 8, 2004

### HallsofIvy

Staff Emeritus
??? All you say is that 8 customers will enter this shop and stay for a period of half an hour. Without more information, we can't say what the probability function is- it might well be that the 8 customers are guarenteed to come at 9 and leave and 9:30!

I could see two plausible probability functions here: the simpler (in concept, probably not in calculation) is that the time each customer enters the shop is uniform over the 3 1/2 hour period from 9 to 12:30.

However, it is more common for problems like this to obey a Poisson distribution. I suspect what you intend here is a Poisson distribution for the number of customers entering, with an average of 8 customers, each staying for 1/2 hour.

3. Aug 8, 2004