Assume that calls arrive at a call centre according to a Poisson arrival process with a rate of 15 calls per hour. For \(0 \leq s < t\), let \(N(s,t)\) denote the number of calls which arrive between time \(s\) and \(t\) where time is measured in hours.

- What is \( \mathbf{E}\big(\,N(3,5)\,\big)\) ?
- What is the second moment of \(N(2,4) \) ?
- What is \( \mathbf{E}\big(\,N(1,4)\,N(2,6)\,\big)\) ?