This probability distribution is used when you have some sort of binary data (such as the toss of a coin, or whether a die rolls a 6), a fixed number of trials (say tossing the coin 10 times) and each trial is independent. The Poisson distribution gives the probability of getting a certain number of 'successes' (e.g. head in a coin toss). The Poisson distribution has two parameters, N (the number of trials) and p (the probability that a single trial is a 'success'). The probability of n successes is then Comb(N,n) p^{n} (1-p)^{N-n}, where Comb(N.n) is the number of combinations of n things out of N = N! / ( n! (N-n)! ). When N becomes large, the central portion of the Poisson distribution is approximately Normal.

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### Links:

- mathworld.wolfram.com: Poisson Distribution
- Wikipedia: Poisson distribution