Let $y \in \mathbb{R}^2$ possess a bivariate normal distribution with mean vector $\mu \in \mathbb{R}^2$ and variance matrix $\Omega = [\omega_{ij}; i, j = 1, 2]$. Find the mean and variance of $y_1$ conditional on $y_2$. Compare this conditional mean with the MMSE linear predictor of $y_1$ given $y_2$. Also compare the conditional variance with the minimized MSE of the optimal linear predictor.