when to sum two random variables

Question

I have typist A who makes errors with rate a errors/page, and B who makes with b errors/page. Now each of em write half of the full publication. I know both are Poisson random variables. In this perspective, how do I know when to add/subtract two random variables? Are there any specific conditions, or it is just an art?

Answer 1

Both typists independently make errors within the publication at a known average rate, with each error independent of the placement of other errors (Poisson Distribution). Thus, other than which half of the publication they occur, the errors made within the publication will be independent of the placement of other errors and be made at an average rate(per publication) that is the sum of the twain (again, a Poisson distribution).

To be clear.   Suppose the publication is $2n$ pages long, and each writes $n$ pages.   Then if the first makes an average of $na$ errors per publication, and the second makes an average of $nb$ errors per publication, then the total errors per the publication is Poisson distributed with mean of $n(a+b)$ errors.