I have a situation where a distribution is dependent on 2 variables, one of which follows the poisson distribution, and the other the normal distribution, and I want to establish the method of calculating the meand and spread for the dependent variable.
I have an algortihm whcih matches names against a bad guy list. The bad guy list is static. The matching algorith can identify 0, 1, 2, or more matches. ie a Poisson distribution. So if I only apply one name I can calcualte the lamda for the distribution.
But, I don't just apply one name I apply many names, once per day, so one day one I might have 100, day 2, 150, etc. The number of names applied each day follows a normal distribution. For this I can calculate the mean and s.d.
What I want to be able to find is the number of matches I can expect each day, and the potential spread. ie combining the 2 distributions
The reason to do this is so that I can determine how many people I need to review the matches, given that it take a set amount of time to review each one. Getting the calculation wrong can be costly, or increase the risks that we may not identify correctly a bad guy becasue we dont have enough staff.