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1. Customers arrive in a certain shop according to an approximate Poisson process at a mean rate of 10 per hour. Let W denote the waiting time in minutes until the first two customers arrive.
(a) How is W distributed?
(b) What is the probability density function of W.
(c) What is the probability that the shopkeeper will have to wait less than 10 minutes for two customers to arrive.
2. Let Z ∼Exp(mean α). Derive E(Z) and Var(Z) using the MGF.
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