The number of customers that arrive at a service station during a time t is a Poisson
random variable with parameter . The time required to service each customer is an exponential random variable with parameter a.
Identify the distribution of the number of customers N that arrive during the service time T of a specificc customer by:
finding the MGF of N
I have found the respective moment generating functions which are:
for the exponential distribution and
Now i have no idea how to combine the results to find the required PDF.
And i cant find anything in my notes about this.