I am trying to understand the relationship between the number of events in a Poisson process, and the waiting times between successive events / inter-arrival times.
Suppose I have a Poisson Process $N(t)$ and also suppose the waiting times between successive events are i.i.d. exponential $(1)$
Here, how can I find the number of events that occurred before a certain time, say $t = 10$ ?
I understand that with this Poisson Process, $N(t)$ ~ Poisson $(t)$, since I assumed that $\lambda$ = $1$ here.
But how to find the number of events before time 10?
Any help is most appreciated. Thank you so much.