The Poisson distribution is a widely used discrete probability distribution in science:

This distribution describes the number of events (x) occurring in a fixed period of time. The events occur with a known average rate corresponding to λ, and event occurrence does not depend on when other events occur. This distribution can be applied to describe the statistics of photon arrival at a detector as illustrated by the following:

a. Assume that you are measuring a light source with an average output of 5 photons per second. What is the probability of measuring 5 photons in any 1-second interval?

b. For this same source, what is the probability of observing 8 photons in any 1-second interval?

c. Assume a brighter photon source is employed with an average output of 50 photons per second. What is the probability of observing 50 photons in any 1-second interval?

P(x) x!