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I do know that the probability density function of beta distribution is $$ \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\displaystyle \mathrm {B}(\alpha,\beta)}\! $$ where $$ {\displaystyle \mathrm {B} (\alpha ,\beta )={\frac {\Gamma (\alpha )\Gamma (\beta )}{\Gamma (\alpha +\beta )}}} $$

Also, I know that support of a function is the subset of the domain containing those elements which are not mapped to zero. But I don't know how do I go about calculating the support for beta distribution.

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    $\begingroup$ What values of the density would you get if either $x$ or $1-x$ were negative?? $\endgroup$ – whuber Mar 24 '19 at 14:38
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    $\begingroup$ In addition to @whuber, have a look here: math.stackexchange.com/a/2355251/614436 $\endgroup$ – CIAndrews Mar 24 '19 at 14:40
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    $\begingroup$ Also Wikipedia. $\endgroup$ – BruceET Mar 24 '19 at 23:29

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