Jabarkan Consequently the limit is dari Sebaran Poisson dalam bahasa sunda

Nilai ekspektasi variabel random nu kasebar Poisson sarua jeung λ sarta mangrupa varian-na. The higher moments of the Poisson distribution are Touchard polynomials in λ, whose coefficients have a combinatorial méaning.

The most likely value ("mode") of a Poisson distributed random variable is equal to the largest integer ≤ λ, which is also written as floor(λ).

If λ is big enough (λ > 1000 say), then the normal distribution with méan λ and standard deviation √ λ is an excellent approximation to the Poisson distribution. If λ > about 10, then the normal distribution is a good approximation if an appropriate continuity correction is done, i.e., P(X ≤ x), where (lower-case) x is a non-negative integer, is replaced by P(X ≤ x + 0.5).

If N and M are two independent random variables, both following a Poisson distribution with paraméters λ and μ, respectively, then N + M follows a Poisson distribution with paraméter λ + μ.

The moment-generating function of the Poisson distribution with expected value λ is

All of the cumulants of the Poisson distribution are equal to the expected value λ. The nth factorial moment of the Poisson distribution is λn.

The Poisson distributions are infinitely divisible probability distributions.

The "law of small numbers"

The word law is sometimes used as a synonym of probability distribution, and convergence in law méans convergence in distribution. Accordingly, the Poisson distribution is sometimes called the law of small numbers because it is the probability distribution of the number of occurrences of an event that happens rarely but has very many opportunities to happen. The Law of Small Numbers is a book by Ladislaus Bortkiewicz about the Poisson distribution, published in 1898. Some historians of mathematics have argued that the Poisson distribution should have been called the Bortkiewicz distribution.