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The likelihood function is

$f(n_1|\alpha,n) = [\frac{n!}{n_1!(n-n_1)!}]\alpha^{n_1}(1-\alpha)^{n-n_1}$

The prior for $\alpha$

$g(\alpha)=(\alpha(1-\alpha))^{-1}$ for $\alpha$ between 0 and 1.

I know that $f(n_1|\alpha,n)g(\alpha)$ is the posterior density. But how can i find the correct form? I suspect it must be the pdf of a beta-distribution.

And how do I calculate the mean and mode afterwards?

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marked as duplicate by whuber Feb 28 at 14:51

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