Suppose that we have a Poisson customer source, which has an arrival rate of 10 customers per hour.
a. What probability distribution does the number of customer arrivals follow at time t?
Write out the probability when we have n customer arrivals at time t.
How many customers are expected during an 8-hour day?
What is the probability of having at 3 customers within one hour?
b. What probability distribution does the nth customer arrival time follow?
Write out is probability density function.
What time do you expect to welcome the 8th customer?
What is the probability you have 8 customers in one hour?
c. What probability distribution does the inter-arrival time follow?
What is the expected inter-arrival time between nth and n+1th customer.