Bernoulli Distribution

Bernoulli Trials

Definition

Bernoulli trials are a sequence of identical experiments with these properties:

  1. All trials are independent
  2. There are only 2 possible outcomes for each experiment, usually "success" and "failure"
  3. For each experiment, the probability of success is the same

Bernoulli Distribution

Definition

Given random variable :

where is the number of successes after independent Bernoulli trial with a probability of success .

The Bernoulli distribution is a special case of the Binomial Distribution, where .

Support and PMF

(support and p.m.f.)

Support

PMF

Expected Value

(expected value and variance)

Equation

Given :