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Probability distributions are mathematical models used to describe the likelihood of different outcomes of a random experiment. Discrete probability distributions are applicable when the random variable takes countable values. Among the most important discrete distributions are the Bernoulli, Binomial, Poisson, and Hypergeometric distributions. Each distribution has distinct assumptions, parameters, and practical applications. The Bernoulli distribution is the simplest discrete probability distribution. It describes an experiment that has only two possible outcomes: success and failure. Let the probability of success be (p), where (0 \leq p \leq 1), and the probability of failure be (1-p). A Bernoulli random variable (X) takes the value 1 for success and 0 for failure. Its probability mass function is given by: ____ ____ _____ ____ ________.
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