Module Catalogue

### EEE2204 : Random Signals and Processes

• Offered for Year: 2017/18
• Module Leader(s): Dr Wai Lok Woo
• Owning School: Engineering
• Teaching Location: Singapore
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0

#### Aims

The aim of this module is to provide students with an appreciation of modern mathematical statistics and probability theory and their various engineering applications. The module will provide the mathematical foundation for these universal theoretical models as the basis for the justification of dealing with data sets that are influenced by chance effects.

#### Outline Of Syllabus

•       Representation of data, mean, standard deviation, variance, random sampling, stratified random sampling, quota sampling.
•       Experiments and outcomes, sets theory for probability theory, relational probability, joint probability, conditional probability, total probability, independence probability, Bayes theorem, permutations and combinations.
•       Random variables, cumulative distribution function, probability density function (pdf), mean and variance of a distribution, Chebyshev’s inequality, Central Limit Theorem (CLT).
•       Binomial distribution, Poisson distribution, Gaussian distribution, distribution of several random variables, unbiased and minimum variance estimator.
•       Sampling theory, estimation of parameters, precision of estimates, confidence intervals for mean of distribution, difference of means, standard deviation, and variance ratio.
•       Estimation theory, covariance, correlation coefficient, goodness-of-fit, contingency table of different random processes.
•       Statistical curve fitting, least-square and minimum mean squared error (MMSE) estimate, standard error estimate, probability interpretation of regression, time-series process prediction.
•       Detection theory, Type-I and Type-II error, maximum likelihood (ML) test, maximum a posteriori probability (MAP) test, Bayes’s test, Neyman-Pearson test.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture241:0024:00N/A
Guided Independent StudyAssessment preparation and completion15:005:00Case study 2.
Guided Independent StudyAssessment preparation and completion15:005:00Case study 1.
Guided Independent StudyAssessment preparation and completion12:002:00Final examination.
Guided Independent StudyAssessment preparation and completion151:0015:00Revision for final examination.
Scheduled Learning And Teaching ActivitiesLecture61:006:00Tutorials
Guided Independent StudyIndependent study431:0043:00General reading; reviewing lecture notes; solving practice problems.
Total100:00
##### Teaching Rationale And Relationship

Lectures provide core material and guidance for further reading. Case studies are explored and set within tutorials.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A70N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Case study1M15Case study 1.
Case study1M15Case study 2.
##### Assessment Rationale And Relationship

The examination provides the opportunity for the student to demonstrate their understanding of the course material. The case studies enable students to demonstrate that they are able to apply this understanding and their analysis and skills to novel situations.