Let X, ...,Xn be a random sample from a GEO() distribution and let the prior distribution of be BETA(2, 2). (i) Find the posterior

Let X, ...,Xn be a random sample from a GEO(θ) distribution and let the prior distribution of θ be BETA(2, 2). (i) Find the posterior distribution π(θ|x) and obtain the Bayes estimator of θ assuming squared error loss. (ii) Compare the obtained Bayes estimator with the MLE for the same data. (iii) Obtain the 95% credible interval for θ.