Twooutcome

Twooutcome refers to a random variable or experiment that can yield exactly two possible outcomes. In probability and statistics, such cases are typically encoded as 0 and 1, representing a binary outcome such as success/failure, yes/no, or event occurs/not occurs. The standard model for a single two-outcome trial is the Bernoulli distribution with parameter p, the probability of the outcome coded as 1.

If X follows a Bernoulli distribution with parameter p, then P(X = 1) = p and P(X = 0) = 1 − p. The expected value is E[X] = p and the variance is Var(X) = p(1 − p). When multiple independent two-outcome trials are conducted, the total number of successes follows a Binomial distribution with parameters n and p, i.e., the sum of n independent Bernoulli(p) variables.

Two-outcome variables are widely used across disciplines. In experimental design, quality control, and survey sampling, binary outcomes are common. In machine learning, binary classifiers predict outcomes like true/false or positive/negative, and logistic regression is a common method for modeling binary outcomes. Hypothesis testing for proportions and other proportion-based analyses also rely on two-outcome models.

Related concepts include binary or dichotomous variables, two-valued logic, and Bernoulli processes. While framed in discrete time, two-outcome models can be extended to sequences of trials or to vector-valued outcomes, and they form the foundational building blocks for more complex probabilistic models.