An example of applications of the Poisson distribution could be the counting of the number of α-particles emitted from a radioactive source in a given time interval. In the limit of n→∞ and for small probabilities y, the binomial distribution approaches the Poisson distribution. Setting λ=ny, with y the probability for an event in the binomial distribution we can show that limn→∞(nx)yx(1−y)n−xe−λ=∞∑x=1λxx!e−λ.