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I have two Beta distributed random variables :

$X_1=B(\alpha_1, \beta_1)$

$X_2=B(\alpha_2, \beta_2)$

What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?

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2 Answers 2

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There are several paper for this problem. See for example:

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You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem

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