Let P^(1) and P^(2) denote transition probability matrices for ergodic Markov chains having the same state space. Let π^1 and π^2 denote the stationary (limiting) probability vectors for the two chains. Consider a process defined as follows: (i) X0=1. A coin is then flipped and if it comes up heads, then the remaining states X1, …are obtained from the transition probability matrix P^(1) and if tails from the matrix P^(2). Is {Xn, n ⩾0} a Markov chain? If p=P{ coin comes up heads }, what is limn

SOLVED: 2.8 A sample realization of random process X(t) is shown in the figure . The time to when the transition from the state t0 the 1 state takes place is random variable that is uniformly distributed between 0 and 2 units: Is the process stationary? Is the process deterministic Or nondeterministic? Find the autocorrelation function and spectral density function for the process'o 1'0 3In addition, determine whether X(t) is ergodic and justify your answer:"o * 2

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