1. (10 points) According to historic weather reports in City A, they never have two nice days in a row. If they have a nice day, they are just as likely to have snow as rain the next day. If they have snow or rain, they have an even chance of having the same the next day. If there is change from snow or rain, only half of the time is this a change to a nice day. (a) Model this problem as a Markov Chain, draw the transition diagram. (1 point) (b) Write down all transient states. Why do you consider them as transient states? (2 points) (d) Write down all recurrent states. Why do you consider them as recurrent states? (2 points) (d) Is this Markov Chain ergodic? Why? (1 points) (e) If you answer YES to question (d), solve the steady-state probabilities for this Markov Chain. Otherwise, explain why we cannot nd the steadystate probabilities. (4 points) 2. (10 points) Consider the transition diagram below for 6 websites: (a) Is this Markov Chain ergodic? Why? (3 points) (b) What is the Google Matrix M for the following diagram? 0920.15) (5 points) (c) What implications can you draw from the structure of this Google Matrix? (2 points) A