February 10, 2004
The Poisson Distribution
If the number of trials is large and the probability is small, the Poisson distribution is a good approximation to the binomial distribution.
Examples include Prussian army officers kicked by their own horses, Geiger counter ticks, and web page hits. In the last case, for example, a large universe of web browsers have a small probability of visiting a given page in a given period of time. The number of visits to that page might well be Poisson.
It was pointed out that a distribution of this sort could be important in a business's plans for handling random arrivals where the arrivals are small probability events for a large population.
The Hypergeometric Distribution
Selling "balls and urns" to econ majors is tough so we will frame the problem in terms of basketball recruiting. Suppose there are 10 players to recruit, but only 4 of those will come if offered a scholarship. The coach will offer 5 scholarships. The key point is that we are drawing players (balls) without replacement.
The general formula for the hypergeometric distribution is
We also had a look at the distribution for 4 offers:
Balls and Urns
We continued our studies of "balls and urns" problems, which includes the binomial, hypergeometric, and Poisson distributions.