This coding exercise is to produce a diagram representation for a given Markov chain. Create two Python

functions: mc diagram used for producing a transition diagram; mc draw for drawing a given diagram.

The specific requirements are as follows.

$$ For function mc diagram

$$ Two inputs: $($i$)$ S: list of states; $($ii$)$ P: the transition matrix.

$$ One output: a graph object from the networkx package that represents the transition diagram.

$$ For function mc draw

$2$

IE $3312$ Probabilistic Operations Research

$$ One input: G: a transition diagram produced from mc diagram

$$ Functionality: draw the input diagram G$.[$You don$$t need to draw the transition probabilities on

arcs$]$

$$ No output.

$$ Hint: you can use networkx.draw to draw a given diagram. The parameter connectionstyle

can change edge to be curvy; the parameter with labels can draw state labels on the nodes.

$$ Test instance: test mc diagram with inputs S and P being the state set and transition matrix of Gambler$$s Ruin $($class example$)$ with p $=0\mathrm{.}52.$ Plot the generated diagram using the second function

mc draw.

$$ Packages and functions you may need to use $($click will lead you to the webpages$)$:

$$ A sample code for drawing Markov diagram

$$ networkx.MultiDiGraph Initialize a graph

$$ networkx.add edge Add edges to a graph

$$ networkx.draw Draw a graph

$$ matplotlib.pyplot.show Show the canvas