Posterior Fair Value from Noisy Signal

A latent "fair value" $V$ is drawn from $V \sim N(0, \sigma_V^2)$ with $\sigma_V = 1$. You observe a noisy signal $S = V + \epsilon$, where $\epsilon \sim N(0, \sigma_\epsilon^2)$ with $\sigma_\epsilon = 2$, independent of $V$. Given an observation $S = 1.5$: 1. Compute the posterior distribution $V \mid S = 1.5$ (find the posterior mean and variance). 2. Compute $P(V > 0 \mid S = 1.5)$.