Question

3. (a) The transition probability of a Markov chain with three states \{0, 1, 2\} is $P = \begin{pmatrix} \frac{3}{4} & \frac{1}{4} & 0 \\ \frac{1}{4} & \frac{1}{2} & \frac{1}{4} \\ 0 & \frac{3}{4} & \frac{1}{4} \end{pmatrix}$ and the initial state distribution of the chain is $P\{X_0 = i\} = \frac{1}{3}$, $i = 0, 1, 2$. Find (i) $P\{X_2 = 2\}$ and (ii) $P\{X_3 = 1, X_2 = 2, X_1 = 1, X_0 = 2\}$.

          3. (a) The transition probability of a Markov chain with three states \{0, 1, 2\} is
$P = \begin{pmatrix} \frac{3}{4} & \frac{1}{4} & 0 \\ \frac{1}{4} & \frac{1}{2} & \frac{1}{4} \\ 0 & \frac{3}{4} & \frac{1}{4} \end{pmatrix}$
and the initial state distribution of the chain is $P\{X_0 = i\} = \frac{1}{3}$, $i = 0, 1, 2$.
Find (i) $P\{X_2 = 2\}$ and (ii) $P\{X_3 = 1, X_2 = 2, X_1 = 1, X_0 = 2\}$.

3. (a) The transition probability of a Markov chain with three states {0, 1, 2} is
P =
< p m a t r i x >
and the initial state distribution of the chain is P{X0 = i} = (1)/(3), i = 0, 1, 2.
Find (i) P{X2 = 2} and (ii) P{X3 = 1, X2 = 2, X1 = 1, X0 = 2}.

Added by Chloe R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Samriddhi Singh

05/18/2022

Step 1

P^2 = P * P = [(3/4, 1/4, 0), (1/4, 1/2, 1/4), (0, 3/4, 1/4)] * [(3/4, 1/4, 0), (1/4, 1/2, 1/4), (0, 3/4, 1/4)] = [(9/16, 5/16, 2/16), (5/16, 7/16, 4/16), (3/16, 9/16, 4/16)] P{x_(2)=2} = (0, 0, 1) * P^2 = 0 * 9/16 + 0 * 5/16 + 1 * 2/16 = 2/16 = 1/8 Show more…

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(a) The transition probability of a Markov chain with threc states {0,1,2} is P=([(3)/(4),(1)/(4),0],[(1)/(4),(1)/(2),(1)/(4)],[0,(3)/(4),(1)/(4)]) and the initial state distribution of the chain is P{x_(0)=i}=(1)/(3),i=0,1,2. Find (i) P{x_(2)=2} and (ii) P{x_(3)=1,x_(2)=2,x_(1)=1,x_(0)=2}. {0,1,2} is (3 0 P = -1v 1 1 2 0 Find(i)P{X=2}and(ii) P{X=l,X=2,X=1,X=2},