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If this sort of help is still available, I have some math I'm working through for a post that I'd love to have checked - a page and a half of fairly basic statistics.
It can be found here (pdf): http://dl.dropbox.com/u/430270/lwalienprisoners.pdf
Thanks!
Here are some initial thoughts. I haven't finished working through it, so more to come:
Perhaps you should specify if the probability of detecting another player is an overall probability or on a per undetected player basis (so when there is only one player they haven't detected yet, when they detect a player it will always be that player they haven't detected)
in the definition of L_K, why is P(K survives turn i) outside the summation? What does i refer to then? Is P(K survives turn i) a constant ? Wont it in general depend on the current state of play?
Thanks for looking at it.
Probability is on a per player basis (ie: each turn, a player has a chance p for detecting each undetected player). I'll edit this so it's more clear.
For LK (as well as LR and L_P), the term outside the summation is essentially (probability the player survives the whole game) * (game length). It's necessary since the game is of fixed length, and the summation is adding (probability of dying on turn x) * (turn x). Consider if the probability of detection is zero, and players will never die - without the term outside the summation, the expected lifetime calculation will return zero.
One more comment:
Is P(K survives turn i) correct? The formula assumes that the chances of surviving are all independent, but I'm not sure that would be true.
I didn't see anything else that stood out to me.
What are you trying to learn or show with the model?
I'll take a look at this in the near future.