Geometric Distribution

We use the Geometric Distribution to answer the following question:

  • Given a probability of success per trial, what is the probability that our first success is on the -th trial, i.e. ?

Geometric Distribution

where is the number of trials required to observe the first success in a sequence of independent Bernoulli experiments.

This can also be formulated as “number of fails before 1st success”.

Suppose ,

  1. Support of :
  2. Probability Mass Function of :

The intuition is simple. You have a probability of failing with over trials, and a probability of success of of succeeding.