# Subject Spotlight: Probability and Random Models

*Welcome to a series covering the variety of electrical engineering subjects available at Melbourne Uni. This series hopes to give those who have not done the subjects a more overall outlook of what the subject entails, tips and more interesting information that is only known by those who have done the subject.*

*Disclaimer: These articles are written from past experiences and may not reflect what the subject is currently like or will be like in the future. The opinions expressed are purely the authors’ and not representative of the Melbourne Uni Electrical Engineers Club or the University of Melbourne. In no way is anything here presented as fact. Do not come complaining to us if after reading something you think the subject is easy and then you fail or if something crucial has changed in the subject.*

Year this subject was taken: 2016

Probability and Random Models is a fairly self contained subject which teaches the required probability knowledge for future engineering applications. Despite this there are only a few engineering examples in this subject and it is purely maths.

Concepts in this subject will be used later in Communication Systems in the form of random noise when communicating across a channel as well as hypothesis testing applied to digital communications. Other subjects that need Probability and Random Models are Advanced Signal Processing, Communication Networks and Wireless Communication Systems.

**Topics:**

- Basic definitions, set theory, permutations and combinations.

- Random Variables (discrete and continuous).
- Multivariate models (More than one random variable).
- Central Limit Theorem.
- Stochastic Processes.
- Markov Chains.
- Hypothesis Testing.

For many of these topics they are defined through the Probability Density Functions, Probability Mass Functions, Cumulative Density Functions, expected values and variance.

**Lectures:**

The lecturer for Probability and Random Models is Prof Margreta Kuijper, lectures are a combination of slides and writing on the document projector. Examples are scanned and uploaded on LMS after the lecture.

There are also plenary tutorials in some weeks (announced on LMS) where Margreta will go through a set of problem questions. In the tutorial she will ask those who are present which questions she should go through.

**Prior Knowledge:**

As previously said this subject is quite self contained, the prerequisites are 1st year Bachelor subjects Linear Algebra and Calculus 2. Signals and Systems is a recommended subject with Laplace transforms closely related to the moment generating function.

Engineering Mathematics and Vector Calculus although not prerequisites are likely to have already been done, they help with integration of vectors and coordinate transformations.

**Workload:**

There is a tutorial every week, with 3 weeks as a tutorial session, the demonstrator going through a set of problems. On other weeks the tutorial is for working on the set assignments done in groups of two. There are 5 assignments usually due the next workshop.

Matlab is used extensively in the assignments.

In the spirit of the subject assignment groups are randomly allocated and change for every assignment. (Not really random) It is a good opportunity to meet new people. Assignments are usually due in the next workshop.

The mid-semester test is similar to the exam at the end of semester. Because it is only 1 hour long the mid-semester is more time constrained than the actual exam.

**Tips:**

Stochastic models = Random models.

It is quite difficult to cram for this exam as they are many different types of questions that can be asked, but only 4-6 questions will be in the exam. It is a good idea to do work throughout the semester as to remember and recognise questions. Not being able to do one question on the exam is a huge loss of marks.

As a result full working out and proper setting out is crucial to get full marks.

You can get all the properties of different probability functions quickly on Wikipedia. Note that the notation of some of the functions will be slightly different so read them carefully.

Most of the topics start off at an adequate pace, the topic Stochastic Processes ramps up in difficulty.

*BY Dennis Nguyen*

*Melbourne University Electrical Engineering Club*

*2016*