Resolve this in R Consider a Markov chain on {0,1,2, ...} such that from state i,...

Resolve this in R

Consider a Markov chain on {0,1,2, ...} such that from state i, the chain goes to i + 1 with probability p, 0 <p <1, and goes to state 0 with probability 1 - p. 

a) Show that this string is irreducible. b) Calculate P0 (T0 = n), n ≥ 1. c) Show that the chain is recurring.

Expert Solution

orchestra answered 2 years ago

Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S. For i ∈...

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Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3} and transition probability matrix (pij ). Let τi = min{n ≥ 1 : Xn = i}, i = 0, 1, 2, 3. Define Bij = {Xτj = i}. Is Bij ∈ σ(X0, · · · , Xτj ) ? Q2. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2, 3}, X0 = 0, and transition...

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Resolve this in R Consider a Markov chain on {0,1,2, ...} such that from state i,...

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Expert Solution

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Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S. For i ∈...

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Q1. Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1,...