📘 probability and stochastic processes
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Markov Chain Analysis
1. **Problem Statement**: Verify properties and analyze the discrete-time Markov chain with transition matrix
$$P=\begin{pmatrix} 0.5 & 0.3 & 0.2 \\ 0.1 & 0.6 & 0.3 \\ 0.4 & 0.0 &