The Beta distribution is a continuous probability distribution often used to model the uncertainty about the probability of success of an experiment.

How the distribution is used

The Beta distribution can be used to analyze probabilistic experiments that have only two possible outcomes:

  • success, with probability χ;
  • failure, with probability 1 – χ .

These experiments are called Bernoulli experiments.

Data collection

Now, suppose that:

  • we perform η independent repetitions of the experiment;
  • we observe κ successes and n — κ failures.

The number of successes obtained in η  independent repetitions of a random experiment having probability of success χ  is a binomial random variable with parameters χ and η.

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