**Subject Code/Name:** MAST20004 Probability**Workload:** 3x1 hour lectures, 1 hour tutorial and 1 hour laboratory class per week

**Assessment:** 4 x 5% assignments, 80% final exam

**Lectopia Enabled:** Yes, with screen capture

**Past exams available:** Yes, from 1999 to 2012 (except 2003) with the answers

**Textbook Recommendation:** Fundamentals of Probability with Stochastic Processes by Ghahramani, but I did not use any

**Lecturer(s):** Prof Peter Taylor

**Year & Semester of completion:** Semester 1, 2013

**Rating:** 4 out of 5

**Your Mark/Grade:** 99 [H1]

**Comments: **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.