Bernoulli distribution
A Bernoulli distribution is a discrete probability distribution for one binary outcome, assigning probability p to one outcome and 1−p to the other.
Fabulous Adventures in Data Structures and Algorithms
A Bernoulli distribution is a probability distribution over two outcomes, conventionally represented by 0 and 1, with an arbitrary probability for one outcome.
- How it is used
- Models binary randomness as a reusable distribution instead of exposing direct calls to a random-number generator.
- How deep it goes
- Explains representation, degenerate cases, GCD normalization, and uniform sampling, but stops short of broader probability theory.
- Examples
- Uses fair, unfair, double-headed, double-tailed, and five-to-seven weighted coins as implementation examples.
- What you can do after
- Build it from scratch in C# with integer weights, normalized odds, singleton edge cases, and a Sample operation.
Read how Fabulous Adventures in Data Structures and Algorithms explains Bernoulli distribution →
Causal AI
The Bernoulli distribution is a discrete probability distribution over a binary outcome with a success-probability parameter.
- How it is used
- Models a binary discrete outcome within probabilistic generative modeling.
- How deep it goes
- Defines Bernoulli as a categorical special case and demonstrates parameterization and log-probability evaluation, without deriving its probability mass function.
- Examples
- Uses heads-and-tails categories, 0-and-1 indices, and Pyro's Bernoulli(probs=0.4) implementation.
- What you can do after
- Apply it via Pyro to instantiate a binary distribution and evaluate an outcome's log probability.
Related concepts
- discrete distributionkind of · A discrete probability distribution assigns probability mass to outcomes in a finite or countably infinite set of distinct values.
- probability distributionkind of · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
- logistic regressionused by · Logistic regression is a statistical classification model that estimates categorical outcome probabilities by applying a logistic or softmax function to a linear combination of input features.
- binomial distributionequivalent to · A binomial distribution is the probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success.
- categorical distributionkind of · A categorical distribution is a discrete probability distribution over a finite set of mutually exclusive categories or outcomes.
- dropoutused by · Dropout is a neural-network regularization technique that randomly suppresses units, connections, or activations during training to reduce overfitting.
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