alias: probability mass function

Real random variable

Discrete random variable

A discrete random variable is a Real random variable with a range 𝑅 of cardinality ≤ℵ0, #m/def/prob that is a set of either finite size or with a bijection to the natural numbers. For any discrete random variable 𝑋 it is possible to define a probability mass function 𝑝𝑋 :ℝ →ℝ such that

from which it follows the series

Similarly we may define the Cumulative distribution function of a discrete random variable (See Variable distribution equivalence).

Distributions

The most common distributions of discrete random variables are

• Bernoulli trial
• Binomial distribution
• Hypergeometric distribution
• Discrete uniform distribution
• Geometric distribution
• Negative binomial distribution
• Negative hypergeometric distribution
• Poisson distribution

#state/tidy | #SemBr