For the Markov decision process of Exercise 1, find the transition matrix corresponding to the stationary policy

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For the Markov decision process of Exercise 1, find the transition matrix corresponding to the stationary policy \(\mathbf{u}\), and calculate \(E_{\mathbf{u}}\left[\sum_{n=0}^{2} R_{n} \mid X_{0}=1\right]\).

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