Question

Q2 (10 points) Let $\{X_n: n = 0, 1, 2, ...\}$ be a Markov chain with state space $\{2, 3, 4, 5, 6, 7\}$ and transition probability matrix $P = \begin{pmatrix} 0 & 1 & 0 & 0 & 0 & 0 \\ \frac{1}{5} & 0 & \frac{4}{5} & 0 & 0 & 0 \\ 0 & \frac{2}{5} & 0 & \frac{3}{5} & 0 & 0 \\ 0 & 0 & \frac{3}{5} & 0 & \frac{2}{5} & 0 \\ 0 & 0 & 0 & \frac{4}{5} & 0 & \frac{1}{5} \\ 0 & 0 & 0 & 0 & 1 & 0 \end{pmatrix}$ Assume that $X_0 = 3$. [5] (a) Find the approximate distribution of $X_{2n}$ as $n$ tends to infinity. [5] (b) Find the approximate distribution of $X_{2n+1}$ as $n$ tends to infinity.

Name: q2 10 points let xn n 0 1 2 be a markov chain with state space 2 3 4 5 6 7 and transition probability matrix p beginpmatrix 0 1 0 0 0 0 frac15 0 frac45 0 0 0 0 frac25 0 frac35 0 0 0 0 frac3 62644
Uploaded: 2024-03-13T16:11:12-08:00
Duration: 1 min 51 s
Channel: Dominador Tan
Description: q2 10 points let xn n 0 1 2 be a markov chain with state space 2 3 4 5 6 7 and transition probability matrix p beginpmatrix 0 1 0 0 0 0 frac15 0 frac45 0 0 0 0 frac25 0 frac35 0 0 0 0 frac3 62644

          Q2 (10 points)
Let $\{X_n: n = 0, 1, 2, ...\}$ be a Markov chain with state space $\{2, 3, 4, 5, 6, 7\}$ and transition probability matrix
$P = \begin{pmatrix}
0 & 1 & 0 & 0 & 0 & 0 \\
\frac{1}{5} & 0 & \frac{4}{5} & 0 & 0 & 0 \\
0 & \frac{2}{5} & 0 & \frac{3}{5} & 0 & 0 \\
0 & 0 & \frac{3}{5} & 0 & \frac{2}{5} & 0 \\
0 & 0 & 0 & \frac{4}{5} & 0 & \frac{1}{5} \\
0 & 0 & 0 & 0 & 1 & 0
\end{pmatrix}$
Assume that $X_0 = 3$.
[5] (a) Find the approximate distribution of $X_{2n}$ as $n$ tends to infinity.
[5] (b) Find the approximate distribution of $X_{2n+1}$ as $n$ tends to infinity.

$q2 10 points let xn n 0 1 2 be a markov chain with state space 2 3 4 5 6 7 and transition probability matrix p beginpmatrix 0 1 0 0 0 0 frac15 0 frac45 0 0 0 0 frac25 0 frac35 0 0 0 0 frac3 62644$

Added by Donna M.

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