Harvard CS181 HW6 (Part 2): HMMs and the Kalman Filter
HW6 Problem 1 (15 pts) swaps the discrete HMM from lecture for a continuous state: the state drifts by Gaussian noise each step, each observation adds more noise, and you derive the mean and variance of the filtering distribution p(zₜ | x₀…xₜ). That is a one-dimensional Kalman filter. The solution is two moves, predict with the transition and then correct with the observation, and the problem hands you both Gaussian identities you need.