Aggregate Loss Model (Actuarial Science)

#1
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!
 

Mean Joe

TS Contributor
#2