In: Advanced Math
Q1. Arrival of customers to a local store may be modeled by a Poisson process with an average of 1 arrival every 10 min period. Each customer on average stays for a time exponentially distributed with mean 15 minutes. This is modeled as a birth-death process.
(i) What assumption is necessary for this process to be modeled as a birth-death process?
(ii) Compute the probability that the number of customers in the store reaches 30, if we have 3 customers at the start.
Pls explain with workings. Thxs