Hey, nice answer. If you are comfortable with the formula (http://en.wikipedia.org/wiki/Expected_value#Discrete_distribution_taking_only_non-negative_integer_v

Hey, nice answer. If you are comfortable with the formula (http://en.wikipedia.org/wiki/Expected_value#Discrete_distribution_taking_only_non-negative_integer_values http://en.wikipedia.org/wiki/Expected_value#Discrete_distrib...): E[N] = Sum_{i >= 0} P(N >= i) then you can reduce some of your calculations and edge considerations. Because the chance that (N >= i) is the volume below the standard simplex, which, as you note, is just 1/i!. Plug in to the above and you get E[N] = Sum_{i >= 0} 1/i! = 1/e