#posterior-mean

Data $x_1, \ldots, x_4$ are iid $\mathcal{N}(\mu, \sigma^2)$ with known $\sigma^2 = 4$, and their sample mean is $\bar x = 2$. The prior on the mean is $\mu \sim \mathcal{N}(0, 1)$. What is the posterior mean $\mathbb{E}[\mu \mid x_{1:4}]$?