Statistics/Probability/Bernoulli Trials

A lot of experiments just have two possible outcomes, generally referred to as "success" and "failure". If such an experiment is independently repeated we call them (a series of) Bernoulli trials. Usually the probability of success is called p. The repetition may be done in several ways:

• a fixed number of times (n); as a consequence the observed number of successes is stochastic;
• until a fixed number of successes (m) is observed; as a consequence the number of experiments is stochastic;

In the first case the number of successes is Binomial distributed with parameters n and p. For n=1 the distribution is also called the Bernoulli distribution. In the second case the number of experiments is Negative Binomial distributed with parameters m and p. For m=1 the distribution is also called the Geometric distribution.