Performance Assessment (Level 0: Problem Extension)



Discrete Probability Models: Markov Chains

The Cat and Mouse

Consider the cat and the mouse problem. Allow the mouse to move as previously outlined, but this time; allow the cat to move. Justify how the properties of the Markov Chain are satisfied. Identify the questions you hope to answer using this process. Construct appropriate one-step transition probability matrix, incidence matrix, state space graph, probability tree, and multi-step probability and incidence matrix. Communicate the information, results and implications of these probabilistic tools and techniques. Identify insights gained through these processes. Propose a new area of application or new questions raised as a result of the model.

 

Task Checklist

 

Student

Criteria

Teacher

Yes No

Yes No

 

 

 

 

 

 

 

1. The interpretation of situation validates a Markov Chain as an appropriate model for the problem.

2. All properties of Markov Chain are clearly identified and valid justifications provided.

3. The identified questions are relevant and go beyond the obvious.

4. Probabilistic tools are appropriately identified and accurately constructed.

5. Each probabilistic tool is interpreted correctly, clearly, and in non-technical language.

6. Insights clearly demonstrate an understanding of the probabilistic tool use.

7. Extensions to the situation clearly connect to new applications and/or new ideas, which lead to further investigations.



 



 



 



 



 









Engin Sungur, Ph.D. & Kathy Meyer, M.Ed. sungurea@caa.umn.mrs.edu & meyerk@willmar.k12.mn.us http://mnstats.morris.umn.edu//me3/me3.shtml