Question
CODE FOR PART 1 AND 2 IF IT IS POSSIBLE MATLAB A worker is trapped in a mine during a mining accident. He starts at
CODE FOR PART 1 AND 2 IF IT IS POSSIBLE MATLAB
A worker is trapped in a mine during a mining accident. He starts at point 1.
In front of him there are three paths. The 1rst leads him back to point 1 (that
is, it leads him to where he started). The second leads him to a point 2. And the
third path leads him to the exit (which we will call point 3). At the point 2 there
are an additional two paths. One of those leads him back to point 2 and the other
leads him back to point 1. To make things worse, this poor guy has amnesia. It is
important to note that the amnesia is what makes this problem a Markov chain.
This is because every time he reaches a point, he is equally likely to choose any of
the paths that lie in front of him because he can't remember anything. Assume
each path takes an hour to travel.
Problem 1. Write a code to simulate the problem and track the number of
hours the worker spent in the mine trying to escape. To do this, make use of
random number generation in Matlab to perform Monte Carlo simulations for a
large number of realizations (say N > 1000). Afterwards, answer the following
questions:
1. What is the expected value of the number of hours the worker spent in the
mine while trying to escape?
2. What is the probability that the worker would get out in 8 hours or less?
3. What is the probability that the worker would spend more than 20 hours in
the mine?
Problem 2. Construct the transition matrix P that describes the Markov
chain. Calculate P2, P3, P4, P5, and P100 in Matlab and explain what the results
mean. (Note: if A = Px, the element Ai;j corresponds to the probability of going
from i to j in x steps.)
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