Question

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]

          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]

$Q.2 The transition probability matrix of a Markov chain {Xn}, n= 1, 2, having 3 states 1,2 and 3 is < b m a t r i x > P = And the initial distribution is P^(0) = (0.7, 0.2, 0.1). Find. i) P(X2 = 3) [2 marks] ii) P(X3 = 2, X2 = 3, X1 = 3, X0 = 2) [2 marks]$

Added by Eric R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

06/15/2022

Step 1

Step 1: To find P(X_2 = 3), we need to consider all possible paths that lead to state 3 at time 2. Show more…

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Q.2 The transition probability matrix of a Markov chain {X_n}, n= 1, 2, having 3 states 1,2 and 3 is $$P = \begin{bmatrix} 0.1 & 0.5 & 0.4 \\ 0.6 & 0.2 & 0.2 \\ 0.3 & 0.4 & 0.3 \end{bmatrix}$$ 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]