Aggregate Loss Model (Actuarial Science)

Asano

New Member
Question:

Let $$S$$ be the random sum of $$N$$ independent frequencies {$${M_i}$$} where $$N$$ is negative binomial distributed with $$r = 5$$ and $$\beta= 3$$ and $${M_i}$$ is Poisson distributed with  = 3.

Find $$F_S(3)$$

Attempt:

I know the formulas for these two distribution, but I am totally lost of how I should approach this. A step by step guide would be much appreciated! Thank you!