This coding exercise is to perform a tiny simulation given a Markov chain transition matrix. Create a Python

function named mc simulation that can simulate a history $($sequence$)$ of states given any transition matrix. The specific requirements are as follows.

$$ Two inputs: $($i$)$ A: a Markov chain transition matrix; $($ii$)$ t: the number of steps to simulate. You can

use the row indices $[0,1,...,$ n $1]$ of matrix A as the set of states.

$2$

IE $3312$ Probabilistic Operations Research

$$ One output: a list of states H $=[$s$0,$ s$1,$ s$2,...,$ st$],$ where si represents the state occurred at time i in

this simulation. You need to randomly pick an arbitrary state from S as the initial state s$0.$

$$ Test instance: test your algorithm with inputs S and A being the state set and transition matrix of

Gambler$$s Ruin $($class example$)$ with p $=0\mathrm{.}52,$ and use t $=10$ as the number of simulation steps. Run

five times of your function, and check how is the simulated history of each run.

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

$$ numpy.shape

$$ numpy.random.choice $($The input parameter p of this function allows you to provide a probability

distribution over possible choices$)$

$$ range

$$ list.append

Note: adding comment in each line of code will receive one extra point given that code runs correctly.