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# NUS Math Module Review: MA3238 ST3236 Stochastic Processes I

Assessment Structure:

20% Homework (3 sets total, 6%-6%-8%)

20% Midterm (Take-Home)

60% Final (Online)

This is a compulsory module for Statistics majors/second majors, and Math majors may also take this module to satisfy their optional major requirements. The module’s topics include review of MA2216, and the remaining topic revolves mainly around Markov chains. This includes first step analysis, Gambler’s Ruin, transient and recurrent states, basic limit theorems, regular transition matrices, double stochastic matrices, reducible Markov chains, time reversible Markov chains, generating functions and branching processes. The main textbook of reference is Introduction to probability models, Sheldon Ross.

Attendance is not compulsory for both lecture and tutorials. All lectures are webcast and recorded, especially due to the COVID-19 pandemic forcing all lectures of modules with >50 students being suspended. I only attended two of the lectures and none of the tutorials. There is a total of three sets of homework, and about 1/3 to 1/2 of the total questions test on MA2216.

Probably due to a large portion of the students taking this module being from the statistics department, while many theorems were introduced, little proofs were explained. As a result, this module is not difficult in the sense that not much understanding is required in order to be able to do the homework and exam questions, much similar to ST2132. Hence, I spent very little time outside homework studying for this module. Thus, this is another “methods” module, but unless one is truly interested, they may not have much takeaway from this module.

Midterm and Final were both open book exams. A well-known fact (which holds true for this semester as well) is that this module includes lots of questions that only require knowledge from MA2216 in their exams. As a result, the exams are generally very easy to score high (perfect score requires one not to commit careless mistakes). This is worsened by the fact that the exams are open-book, so the bell curve for this module is extremely high. I scored mostly full marks for HW and 56/60 for midterm, and performed very well in final. Regardless, I scored a disappointing grade.

While this module provides a gentle introduction to Markov chains (which is pivotal for those interested in more advanced probability theory), do not expect a very rich and rigorous course from this module. Further self-study may be needed to prepare oneself for more advanced theory.

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