Given a hidden Markov Model (HMM) diagram in Figure  to represent weather in Jakarta in the past three months. The diagram in Figure  shows the process of predicting whether someone will be walking, shopping, or cleaning on a particular day based on whether the day is rainy or sunny. In the diagram, two hidden states are rainy and sunny; while the observed states (activities during corresponding weather) are shopping, walking, or cleaning. Based on observation, someone has the following activity sequence: shop, walk, and clean. What is the most likely weather (the hidden states: Rainy or Sunny) sequence, given such activity sequence. Answer this question using Viterbi algorithm and draw weather hidden states sequence using the Trellis diagram.

 

Walk 0.5 Rainy 0.3 Start 0.5 0.3 Shop 0.7 0.2 0.5 Sunny 0.7 0.1 Clean