Posterior Distribution from Beta Density with Exponential Prior Let $X_1,...,X_n$ be iid random variables with a common density function given by: $f(x\theta)=\theta x^{\theta1}$ for $x\in[0,1]$ and $\theta>0$. Put a prior distribution on $\theta$ which is $EXP(2)$, where $2$ is the mean of the exponential distribution. Obtain the posterior density function of $\theta$. Do you recognize this distribution? Clearly $f(x\theta)$ is a beta distribution. So this implies that the posterior distribution is $$f(\thetax)\propto f(x\theta)\pi(\theta)=\frac{\theta x^{\theta1}e^{\theta/2}}{2}$$ But I don't really recognize the distribution at all. Was my calculation incorrect? If not, what is the name of this distribution? 
Looks like a gamma. 
Was it you that got this answered over at Stack Exchange? Are you all set now? 
posterior = ass ? 
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