The probability mass function (”PMF”) describes the probability law of a discrete [[Random Variable]]. This means that it specifies the probability $\mathbf P$ that the r.v. $X$ will take some specific value $x$. We denote this by $p_X(x)$. ^ac7640 $ p_X(x)=\mathbf P(X=x) $ ![[probability-mass-function.png|center|400]] The [[Probability Axioms#Axioms|probability axioms]] for single probabilities, have to hold for a PMF as well: - *Non-negativity:* The probability for every possible $x$ has to be non-negative. $ p_X(x) \ge 0 $ - *Normalization:* The probabilities of all possible $x$ have to sum to $1$. $ \sum_x p_X(x)=1 $