The discrete geometric distribution applies to a sequence of independent Bernoulli experiments with an event of interest that has probability p.
If the random variable X is the total number of trials necessary to produce one event with probability p, then the probability mass function (PMF) of X is given by:
and X exhibits the following properties:
If the random variable Y is the number of nonevents that occur before the first event (with probability p) is observed, then the probability mass function (PMF) of Y is given by:
and Y exhibits the following properties:
| X || number of trials to produce one event, Y + 1|
| Y ||number of nonevents that occur before the first event|
| p ||probability that an event occurs on each trial|