4) Given a Markov model X X2 X3 , what is assumed to be true about the relationship of probabilities of state transitions? That is, how can we simplify P(X1, X2 , X3 )? (4pts) (This should be a very simple equation or one sentence.) 5) HMM: Is the weather outside frightful? Based on experience, I have the belief regarding the probability that it will be raining tomorrow based on whether it was raining today. I've been stuck in my office grading, so I haven't been able to go outside and check the weather, but I can see people walking around on the Great Lawn. Based on experience, I also have a belief regarding the probability of seeing an umbrella based on whether it is raining or not. I have encoded these beliefs in the following two tables. R Rt-1 P(R4+1Rc) R U. P( UR) +r +r 0.7 +r +u 0.9 +r -r 0.3 +r -u 0.1 -r +r 0.3 -r +u 0.2 -r -r 0.7 -r -U 0.8 a) Assuming that it was raining on Thursday, and draw a graphical representation of the Hidden Markov Model for the above scenario for Thursday - Sunday, and label the hidden state and observation states. 4) Given a Markov model X X2 X3 , what is assumed to be true about the relationship of probabilities of state transitions? That is, how can we simplify P(X1, X2 , X3 )? (4pts) (This should be a very simple equation or one sentence.) 5) HMM: Is the weather outside frightful? Based on experience, I have the belief regarding the probability that it will be raining tomorrow based on whether it was raining today. I've been stuck in my office grading, so I haven't been able to go outside and check the weather, but I can see people walking around on the Great Lawn. Based on experience, I also have a belief regarding the probability of seeing an umbrella based on whether it is raining or not. I have encoded these beliefs in the following two tables. R Rt-1 P(R4+1Rc) R U. P( UR) +r +r 0.7 +r +u 0.9 +r -r 0.3 +r -u 0.1 -r +r 0.3 -r +u 0.2 -r -r 0.7 -r -U 0.8 a) Assuming that it was raining on Thursday, and draw a graphical representation of the Hidden Markov Model for the above scenario for Thursday - Sunday, and label the hidden state and observation states