MATH 220 Week 4 Discussion

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Week 4 Forum: Vector Spaces / Markov Chains in Real Life

Markov Chains in Real Life

Markov Chains can be used as mathematical models of real-world situations found in biology, business, chemistry, communications, engineering, physics, weather forecasting, and other applications. Markov Chains are used when you are repeating an experiment or measurement many times in the same way, and the outcome of each trial depends only on the immediately preceding trial.

This week, let’s talk about vector spaces and how they are used in Markov Chains. Markov Chains are used in business, science and/or the military. What are some typical real world situations where you find Markov Chains being used? Pick one such situation and describe it in some detail. What was the most interesting thing you learned about how Markov Chains are being employed?

Be sure to pick a situation to discuss that nobody else has explored in depth yet. Put the application you chose to explore in depth in the subject line heading of your initial post (for example, “Markov Chains in weather forecasting”).

Sometimes students will create an original math homework-type example as it applies to a particular situation, and even work out the numbers, but not do any internet research. Note, however, that the intent of this forum is to do outside research each week and find an application online that you were unfamiliar with, then describe that application in your post. So you will always have outside sources to cite.

Our textbook in section 4.9 lists some specific ideas about situations where Markov Chains are employed, in the examples and homework problems, both in the e-book and in MyMathLab. But probably the best source of information is the internet. When you search online, some good websites to try are (but don’t limit yourself to these, there are many other websites you can use):

http://www.sosmath.com/matrix/markov/markov.html

http://dept.stat.lsa.umich.edu/~ionides/620/notes/markov_chains.pdf

http://en.wikipedia.org/wiki/Examples_of_Markov_chains

http://www.math.ucla.edu/~pejman/intro2prob/LiveMeeting10.pdf

http://www.cs.princeton.edu/courses/archive/spring12/cos423/bib/MarkovChains-3.pdf

Be sure to include the source(s) you use in your post.

Instructions: Your initial post should be at least 250 words. In addition, please respond to at least 2 other students. Your responses should help develop discussion around the topic/feedback that your classmate presented. Responses to students should be a minimum of 100 words each.