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Markov chain question: Let { X,, n = 0, 1, 2, ...} be a Markov chain. Show that the process of pairs { (Xn, Xn+1), n = 0, 1, 2, ...} is also a Markov chain. Let (X_n, n= 0,1,2,.) be a Markov chain. Show that the process of pairs ((X_n, X_(n+1)), n=0,1,2,..} is also a Markov chain.Consider a Markov chain { Xn } with state space S = {0, 1, 2} and transition matrix P = O ON Let the mapping f : S - S satisfy f(0) = 0 and f(2) = 1 and assume that f(1) # f(2). If Yn = f(Xn), then when is {Ym} a Markov chain? Is {Y, } always a Markov chain? In other words, are functions of Markov chains always Markov chains?3.3. Thousands of people are going to a Grateful dead concert in Pauley Pavil- lion at UCLA. They park their 10 foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on (0, 10). In the long run, what fraction of the street is covered with cars