Let $N$ be the number of wars a country $C$ has participated in since year $Y$. Suppose the times of the starts of these wars form a Poisson process with parameter $\mu$ from $Y$ to the present. What is the distribution of $N$?
My intuition is that $N \sim \text{Poisson}(\mu)$ but I am not certain. Any suggestions will be deeply appreciated!
If the parameter is the rate $\mu$ at which events (traditionally called "births") happen, then $N$ is Poisson distributed with mean $\mu$ times the amount of time the process has been running.