An introduction to the Poisson distribution. I discuss the conditions required for a random variable to have a Poisson distribution. work through a simple calculation example, and briefly discuss the relationship between the binomial distribution and the Poisson distributions.

Plutonium-239 example (an average of 2.3 radioactive decays per second).

Finding the probability of exactly 3 radioactive decays in a 2 second period:
dpois(3,2*2.3)
[1] 0.1630676

Finding the probability of no more than 3 radioactive decays in a 2 second period:
dpois(0,2*2.3)+dpois(1,2*2.3)+dpois(2,2*2.3)+dpois(3,2*2.3)
[1] 0.3257063
or
ppois(3,2*2.3)
[1] 0.3257063