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@jemoka / Jemoka Knowledge Base / wiki/concepts/probability_mass_function.md
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--- title: "probability mass function" type: concept related: [Random Variables, Probability Mass Function] source: https://www.jemoka.com/posts/kbhprobability_mass_function/ confidence: high status: active --- PMF is a function that maps possible outcomes of a discrete random variables to the corresponding actual probabilities. For random variable \(Y\), we have: \begin{equation} f(k) = P(Y=k) \end{equation} and \(f\) is a function that is the PMF, which is the mapping between a random variable and a value it takes on to the probability that the random variable takes on that value. Shorthand \begin{equation} P(Y=k) = p(y), where\ y=k \end{equation} its written smaller \(y\) represents a case of \(Y\) where \(Y=y\). Properties of PMD \begin{equation} 0 \leq P(x) \leq 1 \end{equation} and \begin{equation} \sum_{}^{} P(x) = 1 \end{equation}