Ononot — In a Bayesian setting, given a likelihood L(\theta|x) \propt

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Inferential Statisticshard

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In a Bayesian setting, given a likelihood $L(\theta|x) \propto e^{-\frac{(x-\theta)^2}{2\sigma^2}}$ and a conjugate prior $\theta \sim N(\mu_0, \tau^2)$ , which of the following is true regarding the posterior distribution $\pi(\theta|x)$ ?