Q.2 The transition probability matrix of a Markov chain \{X_n\}, n= 1, 2, having 3 states 1,2 and 3 is
$\begin{bmatrix} 0.1 & 0.5 & 0.4 \\ 0.6 & 0.2 & 0.2 \\ 0.3 & 0.4 & 0.3 \end{bmatrix}$
$P =$
And the initial distribution is $P^{(0)} = (0.7, 0.2, 0.1)$.
Find.
i) $P(X_2 = 3)$ [2 marks]
ii) $P(X_3 = 2, X_2 = 3, X_1 = 3, X_0 = 2)$ [2 marks]