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(Solved): Let x_(1),dots,x_(n) be a random sample from Bernoulli (\theta ), where 0<\theta <1 us unknow ...
Let
x_(1),dots,x_(n)be a random sample from Bernoulli
(\theta ), where
0<\theta <1us unknown. Suppose it is known that
\theta ?Uniform
(0,1). Find the Bayesian estimator for
\theta . Solution: The prior distribution is We also know that
T=is sufficient for
\theta (show by FNFT) and that
T?(show by mgf technique) Thus, the posterior distribution is
