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Math 2740 – Fall 2023

Assignment 11

Computer Part

Due Friday, December 01 at 12:00 (noon)

General instructions/remarks

1. This assignment consists of two parts:

❼ the written part consists of long form answers to mathematical problems. Solu-tions to this part are returned using Crowdmark.

❼ the computer part (this document) is answered using a jupyter notebook or RMarkdown file. Solutions to the computer part are returned using UMLearn. See specific instructions below.

2. Late assignments will not be accepted and will be given a mark of zero. UMLearn timestamps submissions and late submissions will be given a mark of zero

3. The mark for Assignment 11 will be a percentage mark consisting of the average of the marks obtained for the written and computer parts.

4. A two part assignment like the present one is only complete if both parts are returned. An incomplete assignment results in a mark of zero.

5. You must complete the assignment BY YOURSELF. Acts of academic dishonesty will be subject to academic discipline.

Instructions/remarks specific to the computer part

❼ Return a single jupyter notebook (.ipynb) or an RMarkdown (.Rmd) file.

❼ If returning an .ipynb file:

– Recall that the notebook must use R.

❼ If returning a .Rmd file:

– This must be proper Rmarkdown, i.e., the code chunks must actually execute when knitting. (And make sure the code actually knits!)

❼ Please make use of the capacity to insert markdown text. In the same way as long form answers need some explanations to be worth full marks, we need to be able to be work what you are doing in order for your code to receive full marks.

Assignment text

Show all the graphs in the Mathematics part of Assignment 11. Compute the equilibrium probability distribution in Q1, where possible. Verify your computations in Q2 and Q3 using “classic” R, i.e., performing the computations directly on the matrices. Then use the package markovchain to verify your computations.