Problem 9 Let P be the one step transition matrix of a Marko

Problem 9: Let P be the one step transition matrix of a Markov chain with states {0, 1,?,n}. Show

Solution

Let A be an event. A convenient notation is P_i(A) = P(A \\ X₀ = i). For example,

P_i( X₁= j) = p_ij

Given the initial distribution lamda, let us treat it as row vector. Then,

P( X₁ = j ) =