Term Taken: 2019 Spring

Instructor (Class A): Prof. Andrej Bogdanov

# Grading Scheme

- Tutorial Participation (+ ESTR Presentation) (12.5%)
- Quizzes (12.5%)
- Midterm Exam (25%)
- Final Exam (50%)
- Homework (0%)

# Textbook

Introduction to Probability (2nd edition), by *Bertsekas* and *Tsitsiklis*.

# Topics Covered

**Probability:**

- Probabilistic Model, Sets.
- Combinatorics.
- Conditional Probability, Independence.
- Discrete/Continuous Random Variables, PMF, PDF, CDF.
- Uniform, Bernoulli, Binomial, Geometric, Poisson, Exponential, Normal R.V.
- Bayes’ Rule, Total Expectation Theorem, Total Law of Variance, Law of Iterated Expectation.
- Expectation, Variance, Covariance, Correlation, Convolution.
- Markov Inequality, Chebyshev Inequality, Central Limit Theorem, Polling.
- Weak Law & Strong Law of Large Numbers.

**Statistics:**

- Sample Mean, (Unbiased) Estimators.
- Bayesian Inference, Maximum a Posteriori.
- Classical Statistics, Maximum Likelihood.
- Mean Squared Errors.
- Confidence Intervals.

# Brief Review

- Worth Taking. (If you are not forced to take it.)
- Average Time-Consuming.
- Pretty interesting.

# Review

This is a required course for most (if not all) engineering majors. It covers some basic probability and statistics which are essential in almost all subfields of engineering. Also, as machine learning becomes increasingly popular, the professor covered more statistics materials this year.

Homework was given weekly, each with 5 problems of fluctuating difficulties. The homework would not be marked, but you had to demonstrate in front of the class on how to solve a problem to gain more participation scores. There were also weekly quizzes, each consisted of one (easy) problem related to the homework. The Midterm Exam was with intermediate difficulty while the Final Exam was more challenging.

Prof. Bogdanov teaches the materials clearly and is willing to answer students’ questions. He has his unique sense of humor and always starts a topic with interesting examples. Though the subject got a little challenging towards the end of the semester(the statistics part), it’s definately worth the time since future engineering courses rely heavily on materials of this course. Plus, to be honest, the study of probability is pretty intriguing itself.

Lastly, a word of advice, If you find some materials hard to understand, READ THE TEXTBOOK AND WORK ON MORE PROBLEMS. If you still find it difficult, maybe you should transfer to another major.

### ESTR2002 Presentation

We had to form into groups of 2 or 3 and gave a 12-minute presentation on some self-selected topics related to probability such as machine learning, information theory, game theory, etc. Maybe I was too stupid, but I found all presentations pretty boring, including ours, so it weren’t competitive and I bet all of us got similar scores.

No other tasks were required for ESTR2002 except the presentation. Even the quizzes, exams are the exact same as regular o’ ENGG2430. So I 100% recommend ELITE students (what a dumb name, Engineering Faculty, please…) to take ESTR2002, it’s a free A-range grade.