What conditions must a probability mass function satisfy?

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probability and statistics
Swiss commemorative stamp of mathematician Jakob Bernoulli, issued 1994, displaying the formula and the graph for the law of large numbers, first proved by Bernoulli in 1713.

For a discrete random variable, a probability mass function, denoted as $f (x)$ , must satisfy two fundamental conditions to be valid:1

Non-negativity: The function must be non-negative for every possible value of the random variable, meaning $f (x) \geq 0$ for all $x$ .1
Normalization: The sum of the probabilities for all possible values of the random variable must equal exactly one.1

These requirements ensure that the function accurately describes how probabilities are distributed across the discrete outcomes of a statistical experiment.1