Module Code - Title:
MA4004
-
ENGINEERING MATHEMATICS 4
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
Rationale and Purpose of the Module:
To provide students with an understanding of the fundamentals of probability and its relation to statistics. To introduce statistical inference through the concepts of estimation and hypothesis testing. To apply these concepts to problems from both daily life and engineering/science.
Syllabus:
The concept of variation - discrete and continuous variables.
Graphical representation of data - frequency tables, histograms, bar charts, piecharts, boxplots.
Descriptive statistics - measures of location and dispersion.
Basic concepts of probability - Frequency interpretation and axioms of probability. Probability of an event. Laws of addition and multiplication. Compound events. Conditional probability. Independence. Bayes Theorem.
Discrete and continuous random variables - expectation and variance, moments.
Discrete probability distributions - Binomial, Geometric, Poisson.
Continuous probability distributions - Exponential, Normal, Uniform distributions.
The central limit theorem.
Statistical inference - interval estimation and hypothesis testing, type I and type II errors, one and two-tailed tests.
Linear regression - testing for an association between two continuous variables.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
1. Describe possible sources of bias in data collection - written examination.
2. Present data using descriptive measures and graphical means (e.g. histograms, bar charts).
3. Use the basic concepts of probability to calculate the (possibly conditional) probability of an event and apply Bayes theorems.
4. Calculate the mean, variance and moments of a random variable given its distribution (for both continuous and discrete random variables).
5. Apply the concepts of the central limit theorem.
6. Calculate confidence intervals for the parameters of a distribution (population mean and proportion).
7. Carry out one and two-sample tests regarding the parameters of distributions and the relation between two continuous variables.
8. Interpret the results obtained from linear regression and understand the limitations of such analysis.
Affective (Attitudes and Values)
1. To develop a critical attitude to the presentation of data in the media
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
The lectures will present the ideas and methods used, together with examples taken from daily life and science/engineering. The tutorials illustrate the lectures based on further examples.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Montgomery D. C. (2003)
Engineering Statistics, 3rd Ed.
, Wiley
Other Relevant Texts:
Walpole R. E. (1998)
Probability and statististics for engineers and scientists, 6th Ed.
, Prentice Hall
Ross S. M. (1987)
Introduction to probability and statistics for engineers and scientists
, Wiley
Stuart M. (2003)
An introduction to statistical analysis for business and industry: a problem solving approach
, Arnold
Daniel W. W. (1992)
Business statistics: for management and economics, 6th Ed.
, Houghton Mifflin
Berenson M. L. (2002)
Basic business statistics: concepts and applications, 8th Ed.
, Prentice Hall
Sincich T. (1996)
Business statistics by example, 5th Ed.
, Prentice Hall
McClave J. T. (1998)
First course in business statsitics, 7th Ed.
, Prentice Hall
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Kevin.Burke@ul.ie