I'm still very confused regarding when to use probability distributions.
For instance, this is the assumptions to use Poisson distribution, according to Wikipedia:
- k is the number of times an event occurs in an interval and k can take values 0, 1, 2, ...
- The occurrence of one event does not affect the probability that a second event will occur. That is, events occur independently.
- The average rate at which events occur is independent of any occurrences. For simplicity, this is usually assumed to be constant, but may in practice vary with time.
- Two events cannot occur at exactly the same instant; instead, at each very small sub-interval, either exactly one event occurs, or no event occurs.
Does that mean that I can assume that any event that follow this assumptions follow a Poisson distribution? If that is the case, why do so many books have exercises mentioning "assume that ... follow a Poisson distribution"? Isn't that unnecessary?
For instance: Let's say I work in a call-centre and I observe that I have 2 calls in the first hour, 3 in the second, 10 in the fourth, 5 in the fifith... I want to know the probability of getting 5 calls in a period of 10 hours. Can I use Poisson?