### Find the properties of the Markov chain with one-step

**Assignment Detail:- ** Question: Consider the following one-step transition probability matrices of two Markov chains:
-a- Use R to calculate P1n with consecutive large n , such as n=1000, 1001, 1002,----Find the following properties of the Markov chain with one-step transition probability matrix P1 based on the results of R together with the theory of Markov chains:• The periodicity of the states;• The stationary distribution-s-, if not unique, show at least two examples;• The long-term properties: convergence of P1n as n→∞;• The conditions of the initial distributions Π-0- such that Π-0-P1n converges as n→∞ even if P1n divergs;• An example of Π-0- with positive elements only -no 0- such that Π-0-P1n converges as n→∞ and the limit of Π-0-P1n
-b- Repeat part -a- for transition probability matrix P2-
Notes:• This question is focused on using R to draw sensible conclusions about Markov chains-• Explain or justify your answers by the results of R and/or the theory of Markov chains-• Formal mathematical proofs are NOT required-• Provide relevant R-codes and outputs that lead to your answers-

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