### What is the distribution of the waiting time

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consider a queuing system with 2 types of customers. type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. type 2 customers arrive according to a Poisson process with a mean rate of 8 per hour. a) find the probability that a type 1 customer arrives before a type 2 does. b) what is the probability distribution of the time between consecutive arrivals of customers (independent of their types?) c) suppose there is one server in the system, which serves both types of customers and the service times follow exponential distribution with a mean of 10 minutes. if a type 2 arrives and the type 1 being served, what is the distribution of the waiting time for this time 2 customer?

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