Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Beta distribution ▷ Probability density function

Theorem: Let $X$ be a random variable following a beta distribution:

\[\label{eq:beta} X \sim \mathrm{Bet}(\alpha, \beta) \; .\]

Then, the probability density function of $X$ is

\[\label{eq:beta-pdf} f_X(x) = \frac{1}{\mathrm{B}(\alpha, \beta)} \, x^{\alpha-1} \, (1-x)^{\beta-1} \; .\]

Proof: This follows directly from the definition of the beta distribution.


Metadata: ID: P94 | shortcut: beta-pdf | author: JoramSoch | date: 2020-05-05, 21:03.