One-Step Prediction with a Persistence Coefficient

A latent state evolves as $x_t=0.9\,x_{t-1}+w_t$ with $w_t\sim N(0,2)$. At time $t-1$ the filtered state is $N(4,3)$. Compute the one-step-ahead predicted mean and predicted variance of $x_t$ (before any observation at time $t$).