Two Plus Two Older Archives  

Go Back   Two Plus Two Older Archives > General Gambling > Probability

Thread Tools Display Modes
Prev Previous Post   Next Post Next
Old 12-04-2005, 04:52 AM
RocketManJames RocketManJames is offline
Senior Member
Join Date: Nov 2002
Posts: 118
Default Poisson and Approximating Binomial

Can someone help me understand this a bit, and tell me if this makes sense at all. Years ago, when I took a probability class, we went over the Poisson distribution, which could be used to approximate the binomial distribution for rare events.

So, say that I've got a fairly rare event (probability of this event occuring is about 1 in 100,000 trials). And, say that I've estimated the probability of this rare event from running 30 million trials and seeing it 300 times.

Now, I have a few questions...

1) Can I use the Poisson distribution to approximate the distribution that I would expect to see if I were to run a large number of trials (N = Large)?

2) Is the reason for using the Poisson Distribution as an approximation, because it is simpler (fewer terms, etc) than the Binomial?

3) Is it possible given the information I gave above to provide some range of error for any estimated distribution? Since P(rare event) was estimated from running 30MM trials and seeing 300 occurrences, can we somehow infer some cloud of error around any distribution we come up with?

I apologize if what I am asking is confusing or if it is way off. I'm just trying to learn here.


Reply With Quote

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

All times are GMT -4. The time now is 05:34 PM.

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.