Markov Assumption: Figure 8 .8a shows a Markov chain for assigning a probability to a sequence of weather events, for which the vocabulary consists of HOT, COLD, and WARM. The states are represented as nodes in the graph, and the transitions, with their probabilities, as edges. The transitions are probabilities: the values of arcs leaving a given state must sum to 1. Figure 8 .8b shows a Markov chain for assigning a probability to a sequence of words w 1 ...w t . This Markov chain should be familiar; in fact, it represents a bigram language model, with each edge expressing the probability p(w i |w j )! Given the two models in Fig. 8.8 , we can assign a probability to any sequence from our vocabulary.