Beta distribution: setup and use case.

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Answer

$X ~ Beta(α, β): support [0, 1], flexible shape controlled by α, β.$
$\operatorname{Var}\; = \;{\alpha}{\beta}\; / \;(({\alpha} + {\beta})^{2}({\alpha} + {\beta} + 1))$
$Very flexible: uniform (α=β=1), U-shaped (α, β < 1), bell (α = β > 1), skewed (unequal α, β).$
$Standard Bayesian prior for probabilities: conjugate to Bernoulli/Binomial — Beta(α, β) + k successes in n trials \to Beta(α+k, β+n-k).$
$Used for A/B testing priors and click-through-rate modeling.$

Check yourself — multiple choice

Support R
Support [0,1]; conjugate prior for Bernoulli/Binomial; E = α/(α+β); flexible shape
Same as normal
Var = 1

Beta: [0,1] support, conjugate for Bernoulli/Binomial in Bayesian inference.

#distributions#bayesian

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