Poisson Process
1. If two independent Poisson processes with rates and are merged, what is the rate of the resulting process?
2. In a Poisson process with rate , if each event is independently classified as Type A with probability p and Type B with 1-p, what is the rate of the resulting Type A process?
3. Why is a Poisson process suitable for modeling the emission of radioactive particles?
4. In the call center, if calls arrive following a Poisson process with = 10 calls/hour, what is the expected number of calls in a 30-minute interval?
5. When splitting a Poisson process, the resulting processes are also Poisson. What property must the splitting mechanism satisfy for this to hold?