Proof: Probability density function of the beta distribution
Index:
The Book of Statistical Proofs ▷
Probability Distributions ▷
Univariate continuous distributions ▷
Beta distribution ▷
Probability density function
Metadata: ID: P94 | shortcut: beta-pdf | author: JoramSoch | date: 2020-05-05, 21:03.
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.
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Sources: Metadata: ID: P94 | shortcut: beta-pdf | author: JoramSoch | date: 2020-05-05, 21:03.