This exercise is in every book, chapter, or section about Bayesian inference.

Suppose that the distribution of y depends on a single parameter, θ. The conditional distribution of the observation y given θ is N(θ, σ2), where σ2 is assumed known. Let the prior for θ also be normal, say, θ ∼ N(μ, τ2).

Derive the posterior of θ.