Poisson and Binomial DistributionsDate: 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? 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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