DataTerminology.comNEW
A distribution for binary outcomes with parameter p.
DESCRIPTION
The Bernoulli distribution models a single binary trial with success probability p and failure probability 1−p. Its support is {0, 1}, with mean p and variance p(1−p). It underlies binary classification likelihoods and logistic regression. Independent sums of Bernoulli variables yield the binomial distribution. Common applications include A/B testing, coin flips, and modeling event indicators.
ALTERNATIVE DEFINITIONS
Wikipedia
In probability theory and statistics, the Bernoulli distribution is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q = 1 − p.
Defines support and complementary probability explicitly.
Statlect
The Bernoulli distribution is a discrete probability distribution for a random variable which takes the value 1 with probability p and the value 0 with probability 1−p.
Concise definition highlighting the two outcomes and probabilities.
RELATED TERMS
Binomial Distribution Beta Distribution Logistic Regression Probability Mass Function Random Variable Dummy Variables Expectation Variance A/B Testing
COMPETING TERMS
RELATIONS
- Broader: Binomial Distribution
- Derivations: Binomial Distribution
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst AI Engineer
EXTERNAL SOURCES
- Wikipedia - Bernoulli distribution
- Statlect - Detailed theory and formulas
- Wolfram MathWorld - Mathematical properties and references
- Khan Academy - Introductory explanation and examples
TOP QUESTIONS
What problems use the Bernoulli Distribution?
It models single binary events like success/failure, click/no-click, or defect/no-defect. It’s foundational for A/B tests and logistic regression likelihoods.
Category: Example
How is the Bernoulli Distribution parameterized?
By a single parameter p, the probability of success (1), with failure probability 1−p. Its mean is p and variance is p(1−p).
Category: Explanation
What is the relationship between Bernoulli and Binomial distributions?
The Binomial distribution is the sum of n independent Bernoulli trials. Bernoulli is the special case of Binomial with n = 1.
Category: Explanation
What is a common mistake with the Bernoulli Distribution?
Assuming independence of repeated trials when data are correlated. Dependence invalidates binomial assumptions and leads to incorrect inferences.
Category: Mistakes
Why is the Bernoulli Distribution still relevant?
Binary outcomes pervade digital products and experiments. It’s the simplest building block for more complex models and statistical tests.
Category: Relevancy
What prior pairs naturally with a Bernoulli likelihood?
The Beta distribution is the conjugate prior for p, enabling tractable Bayesian updates with closed-form posteriors.
Category: How-To
What is a competing concept to Bernoulli Distribution?
The Categorical Distribution generalizes Bernoulli to multiple categories. Use it when outcomes exceed two classes.
Category: Alternatives
How do I generate Bernoulli samples?
Draw u from Uniform(0,1) and return 1 if u < p, else 0. Most libraries provide a Bernoulli sampler directly.
Category: How-To
What is the biggest misunderstanding about Bernoulli data?
Treating proportions as normally distributed without checking sample size; small samples may need exact or binomial-based methods.
Category: Misunderstanding