# ECE2191 - Probability models in engineering - 2017

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Engineering

Organisational Unit

Department of Electrical and Computer Systems Engineering

Coordinator(s)

Professor Zixiang Xiong (Clayton)

Dr Mohamed Hisham (Malaysia)

Unit guides

Offered

Clayton

• Second semester 2017 (Day)

Malaysia

• Second semester 2017 (Day)

## Synopsis

This unit will introduce fundamental concepts of probability theory applied to engineering problems in a manner that combines intuition and mathematical precision. The treatment of probability includes elementary set operations, sample spaces and probability laws, conditional probability, independence, and notions of combinatorics. A discussion of discrete and continuous random variables, common distributions, functions, and expectations forms an important part of this unit. Transform methods, limit theorems, convergences, and bounding techniques are also covered. Special consideration is given to the law of large numbers and the central limit theorem. Markov chain, transition probabilities and steady state distribution will be discussed.

Application examples from engineering, science, and statistics will be provided: The Gaussian distribution in source and channel coding, the exponential, Chi-square, and Gamma distributions in wireless communications and Bayesian statistics, the Rayleigh distribution in wireless communications, the Cauchy distribution in detection theory, the Poisson and Erlang distributions in traffic engineering, queuing theory and networking, the Gaussian, Laplacian and generalised Gaussian distributions in image processing, the Weibull distribution in high voltage engineering and electrical insulation, Markov chain in queuing theory, and first-order Markov process in predictive speech/image compression.

## Outcomes

On successful completion of this unit, students will be able to:

1. Describe random variables including probability mass functions, cumulative distribution functions and probability density functions including the commonly encountered Gaussian random variables.
2. Characterise the distributions of functions of random variables.
3. Examine the properties of multiple random variables using joint probability mass functions, joint probability density functions, correlation, covariance and the correlation coefficient.
4. Estimate the sample mean, standard deviation, cumulative distribution function of a random variable from a series of independent observations.
5. Describe the law of large numbers and the central limit theorem, and illustrate how these two theorems can be employed to model random phenomena.
6. Calculate confidence intervals and use this statistical tool to interpret engineering data.
7. Apply probability models to current engineering examples in reliability, communication networks, power distribution, traffic and signal processing.

## Assessment

Continuous assessment: 40%

Examination (2 hours): 60%

Students are required to achieve at least 45% in the total continuous assessment component (assignments, tests, mid-semester exams, laboratory reports) and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit.

3 hours lectures, 3 hours laboratories/tutorials and 6 hours of private study per week.