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.
Week 2 is about probability: conditional probability and Bayes' rule turn evidence into probabilities; a Bayesian network uses arrows to split a joint probability into one conditional probability table per node, inference by enumeration is exact but slow, and rejection sampling and likelihood weighting approximate it with samples; a Markov chain describes a state that changes over time with a transition model, and a hidden Markov model adds a sensor model to work back from observations to states you cannot see. With time links for every section, plus the approach and checks for the Heredity and PageRank projects.