16. Suppose Sam built a robot with five sensors and wanted to keep track of the location of the robot, and built a hidden Markov model (HMM) with the following structure (which repeats to the right):

(a) What probabilities does Sam need to provide? You should label a copy of the diagram, if that helps explain your answer.

(b) What independence assumptions are made in this model?

(c) Sam discovered that the HMM with five sensors did not work as well as a version that only used two sensors. Explain why this may have occurred.