# Posterior distribution of Bernoulli distribution

by Aditi Akolkar   Last Updated September 12, 2019 02:19 AM

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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