intuitive proofs can be formal too

Let N ~ Poisson with mean mu.
Let X|N=n ~ Binomial(n,p).

Show that X ~ Poisson with mean p*mu.

source: STAT560 - Assignment 2, Problem 2

What most people call a "formal" proof (and what appears in the solution linked) involves writing down the relevant pdfs and working out infinite sums.

I prefer to prove this by simple intuitive logic:( Read more... )