MAST20004: Probability

4x5% Assignments, 3hr 80% Exam

Xi was an absolutely amazing lecturer, coordinator, and warm and genuine human-being. His assignments were often extremely challenging, but I gained a lot from them. He focused on building up a rigorous intuition of the subject from scratch, and developed the subject in a fantastic manner whilst providing useful resources and lecture-by-lecture supplementary notes. My tutor was also excellent, very engaged, passionate and knowledgeable, and we often spent a large amount of the class chatting about further Probability. Stochastic processes was very interesting, it’s a shame we didn’t go into more detail, but Stochastic Modelling is more the subject for that.
Overall, Probability was an immensely interesting and satisfying subject that I’m incredibly glad I took. The exam was very fair and straightforward with Xi, with no surprises. Each of the topics covered in Probability are quite interesting, and the subject definitely does have quite a rapid pace, so it's important to keep up to date (although I admit I did almost none of the Problem Book for the subject). Probability is a wonderful subject, and in my opinion, far less difficult than the reputation it has acquired.

Xi Geng

Yes, many, and with solutions

5/5

Fundamentals of Probability by Saeed Ghahramani recommended. Personally I did not find it useful, and I think the lecture slides and lectures are plenty sufficient.

3x1hr Lecture, 1x2hr Tutorial

2020 Semester 2

95 H1

4 written assignments due every three week during semester each contributed to 5% (total 20%), a 3-hour written examination (80%).

The first assignment is quite easy while the other three are much more difficult. There are at least 4 (usually 5 or 6) questions in each assignment, only two of them will be selected to mark. It's a good idea to redo the similar tutorial questions and discuss with your friend. From this year's feedback I think the relatively easy ones are more likely to be marked (or at least they will leave the most difficult one out). Hence despite the rather time-consuming process of doing the assignments (roughly two nights each for me and similar for my friends) most people seems to get good overall marks from them.

Probability and Statistics from semester 2 are compulsory for actuarial students, so there are fair share of commerce students in this subject, I was in Dr Fackrell's stream (stream 2) and rarely listened to Dr Ross's recording since they have rather different teaching & approaching styles imo. It's actually kinda interesting that some of my friends in stream 1 believed Dr Fackrell is better at teaching and friends in stream 2 thought exactly the opposite, so in the last few weeks of the semester there were quite a lot students choosing to go to the other stream.

The prerequisites for this subject are just Calculus 2 and Linear Algebra, but I think it needs at least some knowledge from vector calculus as well as real analysis. Have done vector calculus last semester and been doing real analysis concurrently this semester, I went through ok with all the proofs and definitions. However, my friend who did probability last year without any knowledge from these two had found herself having difficulties a lot of times.

If we've been allowed to describe the exam in one word I believe a lot of people will choose HARD. I've never felt completely lost in a exam like this, at last I even started calculating if I could pass. The exam allowed you to bring in a double sided A4 cheat sheet and it had the similar difficulty level as the assignments with a few harder parts for last several questions. I think it's really aiming to test if you actually understand all the concepts taught in the semester instead of just knowing how to applying the method. So it's really important to know how each distribution behaves, how to determine which one to use and how to manipulate them under certain circumstances. Simply cram all the formulas into cheat sheet won't help you in doing these exam questions maybe except the first three points:) Anyway I believe the only possible way to do well in this exam is to study every single page of the lecture note over and over again until you could understand each proof well, then try to make a mind map for the whole subject and do as much as questions as possible.


All in all I think this is a much more theoretical subject than I expected and the contents are rather intelligently demanding comparing to other second year math subjects I've done so far, it certainly needs a lot of self learning, maybe as well as a much more understandable teaching style.

Yes, both streams with screen capture.

Dr Nathan Ross for stream 1, Dr Mark Fackrell for stream 2.

The first few weeks of this subject is quite relaxing, just like doing probability questions from high school. We also learnt about both discrete and continuous variables, their distribution function (cdf) and probability mass/density function (pmf/pdf). Then coming into some special distributions like binomial, geometric, negative binomial, normal, exponential and gamma, a large proportion of class will be used in proving/deriving these distributions' pmf/pdf as well as their expected values and variances, which can seem boring at the time. There were far too less examples in this part and many students I know (and myself as well) find it quite hard to put theorem into application. Then we'll learn bivariate random variable and their joint/marginal/conditional pmf/pdf. We'll study the transformation i.e. functions of single random variable and bivariate random variable. One very important topic is about condition on RV and how to derive expected values, variance and probability under this circumstance, there will be a great proportion of final exam focusing on this and using any of the distributions that were previously learnt. Then we'll learn about probability generating function and moment generating function, which extending to the last topic of branching process.

The lecture is heavily based on proof like I mentioned before and can be really hard to keep up as Dr Fackrell usually went quickly between steps and rarely gave enough justification, I usually needed one more hour after each class to understand how each step of his proof worked. The order of topics is also a bit confusing at the time since Dr Fackrell actually taught each of them quite separately and never really engaged in explaining how to connect them, it's not until SWOTVAC when I was revising the whole subject and finally came up with an (not so clear) understanding of how each topic connects with each other.

Yes, 6 past exams from 09 to 15, all with solutions and all assignments from 14 & 15 with answers.

The first hour of tutorial is just typical math tutorial where you do questions with a table of other students on whiteboard and the tutor hovering around to help you if you got stuck. The tutorial questions can be very good and much needed exercises for better understanding of all the definitions, since there aren't many examples given in the lectures. The second hour is joining by another tutorial and doing tasks related to lecture contents in a computer lab, there's no lab test in this subject so not many people pay a lot attention to the computer lab, but there will be a question in final exam entirely relied on contents from lab (though not a lot marks), this year it's the second last question with 6 marks out of 100.

3.5 Out of 5

Lecture notes can be purchased from co-op, there's also a pdf version on lms. Recommended textbook is Fundamentals of Probability with Stochastic Processes, 3rd Edition by S Ghahramani (Pearson Education, Inc. Upper Saddle River, NJ, 2005). There are a few copies at ERC, you could also find pdf version (with solutions) on google (if anyone need it feel free to pm me).

3 x one hour lectures per week, 1 x one hour practice class per week, and 1 x one hour computer laboratory class per week.

2016, Semester 1

H2A (79)

4 Assignments due in weeks 3, 6, 9 and 12 (20%)
3 hour exam (80%)

This subject is a nice introduction to probability and its applications. If you really enjoyed probability in VCE, you may very well enjoy this subject too. However most of the people who took this subject took it because it was compulsory for them. It was very well run, there were no issues at all apart from a few lectures not being recorded.

In all honesty, if you're quite confident in your mathematical ability, you could afford to slack off in the first few weeks of the subject as the content isn't too challenging. As stated in a previous review, the content starts to ramp up around Negative Binomial, week 5. Things can get pretty confusing and if you're not up to date then lectures can seem much more challenging than they are, and there is no real point in going to tutorials. The content starts to slow down at generating functions and the last few weeks are pretty easy-going.

Nathan Ross is a good lecturer. I thought he explained concepts very well and encouraged a different way of thinking when approaching problems. However, at times I feel that much of what he says isn't very relevant to the tutorials, which can make them very difficult to solve on their own. This isn't necessary a criticism, but perhaps something they could improve upon in future years. I recommend going to the lectures as they you'll be able to see both the notes written by Nathan and the slides, whereas at home you'll only be able to see the notes, however lectures can be placed at bad times (e.g 4:15 Fridays this year), so you can easily fall into the habit of not going to them. I felt that I absorbed much more when I was there in person than by watching them at home.

The class tutorials were okay. Just your standard maths tutorial where you stand around with others solving problems on the boards. If you're not keeping up to date with the lectures, the tutorial problems can be too hard to solve while in class, or at least each one would be very time consuming. I recommend to have a go at solving them before the tutorial so that you can make decent progress with your group. Also check out the video consultations for select questions if you're stuck, Robert Maillardet is very good at explaining the thought process that is needed to solving problems.

I thought the computer lab tutorials were very interesting. They involved looking at some practical applications of probability in MATLAB, combining the methods learnt in lectures with the tutorial problems. There was no assessment during the semester on these computer lab tutorials, which I really think is a shame, as the content was very interesting and it only encouraged people to bum around in these tutes. Working in groups is the best way to get the most out of these tutorials.

There were four, evenly spaced out assignments, each worth 5% each of your total mark. Each comprised of a few questions, with each question having a few parts. Similar to other maths subjects, only some of the questions are marked. While assignment 1 was very easy, the remaining 3 had challenging parts to them and I found it really helpful to discuss and solve the problem with friends.

Yeah...the exam...A fairly challenging one, that really makes you think for the entirety of the three hours. This is not something you easily cram, but rather rewards you for the amount of work you put in throughout the semester. Questions very much resemble assignment questions in style, with usually the last part of the last few questions being quite hard. You're allowed one A4 double-sided "cheat sheet" into the exam, which was really useful since there are a large number of formulae, distributions, rules that would otherwise need remembering. It also helps to put in some past exam/tutorial/assignment questions on your sheet (if you have any space) to help you answer some of the trickier questions.
Overall, this was a good subject. How much you enjoy this subject will most likely depend on whether you like probability in the first place. So if you are one of those people, and looking for a 2nd year maths which does not contain much proof, this is the subject for you.

Yes, but only what the lecturer writes down on blank pages is shown, not the slides themselves.

Nathan Ross

Yes, 5 exams with solutions.

3.5 out of 5

Don't know the textbook, don't think it's necessary to have

3 x 1 hour lectures per week, 2 x 1 tutorials per week (one in class tutorial followed by a computer lab session)

2015, Semester 1

75(H2A)

4 x 5% assignments, 80% final exam

As its name, this subject introduces the basic concepts of probability. If you are undertaking Actuarial Studies, you have to do this subject instead of MAST20006 Probability for Statistics. If you are not an actuarial students, you should note that the prerequisite of MAST30020 Probability and Statistical Inference is either to pass this subject or to get a H2B or above in Probability for Statistics (Probability for Statistics is non-allowed subject of Probability)

Lectures:
This subject is not divided in chapters or modules, but I like to divide this subject into some parts:
1. Defining Probability: probability axioms, conditional probability, independence, law of total probability, Bayes’ formula, discrete & continuous random variables (RVs), expectation, variance and higher moments of a RV.
2. Special Probability Distributions: Discrete distribution (Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, discrete uniform distribution) and Continuous Distribution (continuous uniform, Exponential, Gamma, Normal distribution).
3. Transformations of Random Variables
4. Bivariate Random Variables: distribution function of bivariate RVs, joint and marginal pmf & pdf, conditional pmf & pdf, bivariate normal distribution, independence of RVs, transformation of bivariate RVs (including convolution theorem), expectation of function of two RVs, Covariance & Correlation, Conditional expected value, Conditional variance and approximations for the mean & variance of functions.
5. Generating Functions and Applications: probability generating function (pgf) and moment generating function (mgf), Chebyshev’s inequality, limiting distributions, law of large numbers, central limit theorem and branching process.
6. Stochastic Processes: Discrete-Time Markov Chain (DTMC)


My Opinion:
This is the first maths subject which made me completely lost in each lecture. The first few weeks were pretty easy, but it got much more difficult starting from Negative Binomial Distribution. As a result, I went to tutorials knowing nothing and ended up sitting down, looking at the whiteboard, which means I learned nothing from each tutorial. The assignments were also pretty hard (except assignment 1) and it took me all night to finish each assignment. It wasn’t until SWOTVAC when I finally understood what was going on and could use my “common sense” in this subject.

This subject relies on Taylor series, which is covered in Real Analysis and Engineering Mathematics. However, both subjects are not the prerequisites thus making those people who haven’t done Real Analysis or Engineering Mathematics a bit confused. Also, to prove some formulae, we often need to change the (in)finite sum to a closed form (eg. change of summation index, binomial theorem, Taylor expansion of exponential etc.), which is one of the major problems for many people. Also, when you start learning bivariate random variable, there will be some vector calculus involved, which is (again) not the prerequisite of the subject. I frequently found my friends having trouble not about the probability concept, but about the vector calculus concept. In my opinion, the vector calculus problem is even harder in this subject because we often deal with piecewise function.

The tutorial was 2 hours, where the last 1 hour was used as a laboratory class. I think the laboratory class was useless since they already gave you the program, and the explanation was not clear at all. Frequently the program was too complex for students who had just learned MATLAB (I have done ESD2, but I still have no idea of how the program works), thus my friends and I did not pay too much attention in almost all computer laboratory classes (although I believe that simulation using computer is very important). There was no computer test, but there was one question on the exam which was based on the concept used in the computer laboratory class.

My advise of how to do well in this subject is to clearly understand your basic probability concept. Make sure you know the difference between pmf, pdf and distribution function. Use analogy to understand your special distribution functions (eg. exponential distribution is the continuous case of geometric). After you understand what is going on in this subject, do your tutorial sheets and past exams with your cheat sheet. (You are allowed to bring a double-sided A4 paper, must be handwritten)
Overall, this is a good and challenging subject, but the computer laboratory content (especially the explanation of the computer lab sheet) should be improved.

Yes, with screen capture

Prof Peter Taylor

Yes, from 1999 to 2012 (except 2003) with the answers

4 out of 5

Fundamentals of Probability with Stochastic Processes by Ghahramani, but I did not use any

3x1 hour lectures, 1 hour tutorial and 1 hour laboratory class per week

Semester 1, 2013

99 [H1]