The Bernoulli distribution is the range of probabilities for two possible outcomes. It is a central statistical concept. This entry describes the Bernoulli distribution and Bernoulli random variables and explains the relationship between the Bernoulli distribution and the binomial distribution.
Suppose a random experiment has two possible outcomes, either success or failure, where the probability of success is p and probability of failure is q = 1 − p. Such an experiment is called a Bernoulli experiment or Bernoulli trial. For a Bernoulli experiment, define a real-valued random variable X which takes two values as: X = 1 if success and X = 0 if failure. Such a random variable X is called a Bernoulli random variable. The probability distribution of X is given by Pr(X ...
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