Hidden Markov Model Bayesian Relation

Question

Hi all this is artificial intelligence class from udacity. I have a question. P(R0)=1 means probability of day0 rainy is is 1. Here is my question P(R2 | H1 G2)? meaning we know I am happy at day1 and grumpy at day2 what is probability it is raining at day2

Answer 1

Some useful data

P(R_2|H_1, G_2) can be reduced to P(R_2|G_2) because there is no given transition coeffs. between moods (this can be discovered for a weather sequence however).

P(R_2|G_2) = P(G_2|R_2)*P(R_2)/P(G_2) = 0.264*0.440/0.320 = 0.363