Question

X_n is a Markov Chain with state-space E = {0, 1, 2}, and transition matrix

0.4 0.2     ?

P = 0.6 0.3    ?

0.5 0.3    ?

And initial probability vector a = [0.2, 0.3, ?]

a) What are the missing values (?) in the transition matrix an initial vector?

b) P(X₁ = 0) =

c) P(X₁ = 0|X₀ = 2) =

d) P(X₂₂ = 1|X₂₀ = 2) =

e) E[X₀] =

For the Markov Chain with state-space, initial vector, and transition matrix as defined above,  discuss how we would calculate the following:

a) P(X₁ = 0, X₂ = 0, X₃ = 1, X₄ = 2|X₀ = 2)

b) P(X₂ = 2, X₄ = 0, X₅ = 1)

Answer 1