# Thread: Show that the Markov chain is irreducible.

1. ## Show that the Markov chain is irreducible.

Show that the following Markov chain is irreducible:

$\displaystyle S=\{0, 1, 2, ..., N\}$
$\displaystyle p(X_{0}=i)=\frac{1}{(N+1)}$ for i=0,...,N

for all state (except 0 and N)
$\displaystyle P_{ij}= \frac{1}{3}$, $\displaystyle j=i$
$\displaystyle P_{ij}= \frac{1}{3}$, $\displaystyle j=i+1$
$\displaystyle P_{ij}= \frac{1}{3}$, $\displaystyle j=i-1$

for state 0
$\displaystyle P_{0j}= \frac{2}{3}$, $\displaystyle j=i=0$
$\displaystyle P_{0j}= \frac{1}{3}$, $\displaystyle j=i+1=1$

for state N
$\displaystyle P_{Nj}= \frac{2}{3}$, $\displaystyle j=i=N$
$\displaystyle P_{Nj}= \frac{1}{3}$, $\displaystyle j=i-1=N-1$

2. Do not give full solutions. This is an assignment question

3. Originally Posted by Langtry
Do not give full solutions. This is an assignment question