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The Bernoulli distribution is a discrete probability distribution for a random variable that takes only two possible values, 0 and 1. Examples of events that lead to such a random variable include coin tossing (head or tail), answers to a test item (correct or incorrect), outcomes of a medical treatment (recovered or not recovered), and so on. Although it is the simplest probability distribution, it provides a basis for other important probability distributions, such as the binomial distribution and the negative binomial distribution.

Definition and Properties

An experiment of chance whose result has only two possibilities is called a Bernoulli trial (or Bernoulli experiment). Let p denote the probability of success in a Bernoulli trial (0 < p < 1). Then, a random variable X that assigns ...

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