update markov chain blog

_posts/2023-07-12-markov-chains.md

@@ -96,7 +96,7 @@ Let $\mu_{i} = \sum_{t \geq 1} t \cdot r_{i,i}^{t}$ denote the expected time to
 
 Here we give an example of a Markov chain that has null recurrent states. Consider the following markov chain whose states are the positive integers.
 
-![Fig. 1. An example of a Markov chain that has null recurrent states ](assets/img/markov_chains/image.png)
+![Fig. 1. An example of a Markov chain that has null recurrent states ](image.png)
 
 Starting at state 1, the probability of not having returned to state 1 within the first $t$ steps is
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@@ -135,7 +135,7 @@ A state $i$ is periodic means that for $s = k, 2k, 3k,...$, $P(X_{t+s}= j | X_t
 
 Consider the two-state “broken printer” Markov chain:
 
-![Transition diagram for the two-state broken printer chain](assets/img/markov_chains/2023-07-22-11-00-52.png)
+![Transition diagram for the two-state broken printer chain](2023-07-22-11-00-52.png)
 
 There are two state (0 and 1) in this Markov chain, and assume that the initial distribution is
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