Grumpy oat lives a simple lite. Some days she is Angry [13) and some days she is Happy (@1. But she hides her emotional state 2;,\" and so all you can observe is whether she expresses x\" = smiles ts]. frowns [t]. laughs {I}. or yells [y]. We start on day :1 = l in the Happy state. z] = Q. and there is one transition per day. The state transition probabilities are The expression probabilities. p{x I z]. are p[s|)=0.5 p(f|@)=(i.l p[f|@}=0.2 p(y|@]=ll2, p[s|)=0.1 pmrsJ=a5 p(r|}=o.2 pmei=a1 {a} What are the starting probabilities g and 113? {b} What is pkg: = @J? to} What is ply; = f}? id} What is p(x1m = y)? is} We observe x1 2x2 2x3 2x4 = f. What is the most likely emotional state sequence (2,1,. .. ,54] that grumpy cat was in? (Hint: Viterbi aigorithm}