The pdf of X | $\theta$ is given by $\theta^x (1- \theta)^{1-x}$

and its prior distribution is given by $p(\theta) \frac {1} {B(\alpha, \beta)} \theta^{\alpha - 1} (1 - \theta)^{\beta - 1}$

where $B(\alpha, \beta) = \int_0^1 x^{\alpha - 1} (1-x)^{\beta -1} dx$

Can someone help me determine posterior distribution of $\theta$ and to show that its a weighted average between the MLE and the prior estimate of $\theta$ under the beta prior?



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