What I have a problem with -- as evidently you do too -- is deriving those formula.

Well, I'm sorry you didn't understand because I wasn't trying to help you convert between programs and formulae (hence why I left that step to you). I was explaining how to derive the most interesting part of the formula at hand (well, verify the derivation in order to understand it, since the formula was already provided).

I was not trying to teach you how to do integration nor how integration correlates to this sampling problem. I have no interest in trying to teach beginning calculus via a web forum.

But it seems your expressed desire "to understand" does not extend to trying to understand 1-exp(1-$inserts/$slots). Perhaps my explanation will assist others on that point.

But my explanation also serves as response to more than one private request you made to me, despite your apparent lack of interest now.

I seriously hope this will not offend you, but suspect it will.

I'm not sure why.