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Inferential Statisticshard
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In a Bayesian setting, given a likelihood L(θ∣x)∝e−(x−θ)22σ2L(\theta|x) \propto e^{-\frac{(x-\theta)^2}{2\sigma^2}}L(θ∣x)∝e−2σ2(x−θ)2​ and a conjugate prior θ∼N(μ0,τ2)\theta \sim N(\mu_0, \tau^2)θ∼N(μ0​,τ2), which of the following is true regarding the posterior distribution π(θ∣x)\pi(\theta|x)π(θ∣x)?