Here is the problem:

Consider the queueing system, there are n customers 1, 2, ...N.

Customer 1 arrives in accordance with a Poisson process with rate Lamda, customer 2 arrives in accordance with a Poisson process with rate Lamda,..., customer N arrives in accordance with a Poisson process with rate Lamda .

What is the distribution in which at least one customer arrive at time t?