Probability mass function

A probability mass function assigns a probability to each possible value of a discrete random variable. Its values are nonnegative and sum to one.

Discrete random variable: A random variable whose possible values form a finite or countably infinite set. A probability mass function assigns probabilities to the values of this kind of variable.
Probability: A numerical measure of the likelihood of an event, ranging from zero to one. Each output of the mass function is the probability of one outcome.
Bernoulli distribution: A distribution on zero and one, with the probability of one set by a parameter. Its two point masses encode the outcomes of a single success-or-failure trial.
Probability density function: A function describing the relative concentration of probability across values of a continuous random variable. Unlike a mass function, a density's value at one point is not the probability of that point.
Support (mathematics): The set of values where a function or distribution is nonzero. The support identifies which values receive positive probability mass.
Random variable: A function that assigns a numerical value to each outcome of a random experiment. The mass function describes the probabilities associated with its possible values.
Binomial distribution: The distribution of the number of successes in a fixed number of independent Bernoulli trials. Its mass function gives the probability of each possible success count.
Mixed distribution: A probability distribution combining discrete point masses with a continuous component. Its point probabilities coexist with density-based probability, unlike a purely discrete mass function.
Cumulative distribution function: A function giving the probability that a random variable is at most a specified value. Summing masses up to a value produces the cumulative distribution function.
Sample space: The set of all possible outcomes of a random experiment. A random variable maps sample-space outcomes to the values whose probabilities are tabulated.

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