Poisson distribution expresses the probability of a number of events
occurring in a fixed period of time if these events occur with a known
average rate and independently of the time since the last event. The Poisson
distribution can also be used for the number of events in other specified
intervals such as distance, area or volume. If the expected number of
occurrences in this interval is λ, then the probability that there
are exactly n occurrences (n = 0, 1, 2, ...) is equal to
λn e-λ
f(n; λ) = ---------
n!
For sufficiently large values of λ, (say λ > 1000), the normal
distribution with mean λ and variance λ, is an excellent
approximation to the Poisson distribution. If λ is greater than about
10, then the normal distribution is a good approximation if an appropriate
continuity correction is performed, i.e., P(X ≤ x), where (lower-case) x
is a non-negative integer, is replaced by P(X ≤ x + 0.5).
When a variable is Poisson distributed, its square root is approximately
normally distributed with expected value of about λ1/2
and variance of about 1/4.