A banker has three different suits she wears to work, a navy blue one, a gray one and a beige one. She never wears the same suit two days in a row. If she wears the navy blue suit one day she always wears the gray one the next day. If she wears either the gray or beige suits one day she is twice as likely to wear the navy blue one rather than the other one the next day. 1) Formalizing the above problem as a Markov chain, draw a transition probability graph. 2) What is the transition probability matrix? Please use the following order of (1) navy blue, (2) gray, and (3) beige for the row and column. 3) Does this Markov chain has a unique steady-state distribution? Why?