The number of quarterly claims an insurance company receives is represented by a random variable $N$ which is poisson distributed at a rate $\lambda \in (0, \infty)$.
With each claim received, let $p \in (0,1)$ be the probability that a related claim is received during the next quarter.
Determine the range and the pmf of the random variable $X$ which represents the number of related claims received in the next quarter. What distribution does $X$ follow?
I think by definition X follows a compound poisson distribution, and I would say the range is $(N(\lambda), \infty)$, but any ideas on how to determine the pmf of X?