This is a question from an old test, taken completely out of context:
"The customers arrive at a shop according to a Poisson distribution with mean $\lambda$ per hour. Each customer takes $1/k$ hours of service. What is the expected value and the variance of the service time for customers arriving within an hour? What is the probability that the service time exceeds $t$ hours?
I am not entirely certain how to approach this question. This is supposed to be a simple Poisson-distribution question, with no Poisson processes or queuing.
Are there any ways to look at this question in a simpler way? What is the general approach here?
Apologies if I am completely misunderstanding this.