A switchboard receives on average 6 calls per hour, with independent arrivals at a constant rate. What is the parameter \(\lambda\) for the number of calls in half an hour?
A Poisson variable \(X\) counts independent events, at a constant average rate, in a fixed interval; its parameter \(\lambda\) is the mean number of events and \(P(X=k)\) the probability of observing \(k\).