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### Poisson and Binomial Distributions

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Date: 02/22/99 at 01:29:53
From: jill
Subject: Poisson and Binomial Distributions

I am just starting statistics and I am having problems understanding
Poisson and Binomial distributions. What are the assumptions made in
these distributions?
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Date: 02/22/99 at 04:47:05
From: Doctor Mitteldorf
Subject: Re: Poisson and Binomial distributions

Think of a binomial distribution in terms of coin flips: If you flip a
coin 3 times, you can have 0, 1, 2 or 3 heads. 0 and 3 occur
comparatively less often than 1 and 2, because there are different
ways to mix up the heads and tails for 1 and 2, but 0 and 3 require
straight, consistent luck. In general, a binomial distribution
represents the probability of getting k heads if you flip a coin n
times.

Think of a Poisson distribution in terms of time sequence of random
events. Imagine that you run the customer service department of a mail
order company with millions of customers. You know that the calls come
in at an average rate of 1 per minute. But in any given minute, you
might have 0 calls or 1 call or 2 calls (these are pretty likely) but
your worst nightmare is that 500 people will all decide to call in that
same minute (unlikely, but possible). In general, you can think of a
Poisson distribution on n and k in this way: if the AVERAGE number of
people calling in one minute is n, what is the probability that in any
given minute you'll get k callers?

Notice that the binomial distribution is 1) bounded at both ends and
2) symmetric. It is bounded because you can never have more than N
heads or less than 0. It is symmetric because the probability of
getting k heads is always the same as the probability of getting k
tails - which is N-k heads.

The Poisson distribution is bounded at the bottom but not the top. You
can never have fewer than 0 calls in a given minute, but you can have
thousands if you're really unlucky in that minute. The Poisson
distribution is asymmetric because it's one-sided in this way.

Of course, this is only a start, but I hope it helps you to have a
mental picture as you read more about the subject and work lots and
lots of examples.

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
College Probability
High School Probability

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