Consider the following example: You are the security guard stationed at a secret underground installation. You want to know whether it's raining today, but your only access to the outside world occurs each morning when you see the director coming in with, or without, an umbrella. A Hidden Markov Model (HMM) of this system, with corresponding transition and emission probability tables, is given below: Rain R-1 1 f Umbrella P(R) 0.7 0.3 Rain, R t f Umbrella, P(U) 0.9 0.2 Rain Umbrella 1+1 Assume that the prior probability of rain is 0.4, i.e., P(R) = 0.4. From the given information, answer the following questions: i. Explain what the four values in the two given tables represent. [4 points] ii. What is the probability that it rains on Day 2? [4 points]