MC3020 - Probability and Statistics

Welcome to Probability and Statistics!

Engineering today operates in an increasingly data-rich environment. This course is designed to introduce you to statistical concepts and methods which will encourage you to operate confidently and effectively in this environment. The course provides an introduction to the presentation, analysis and interpretation of quantitative data in an engineering context. Topics include the use of R program to construct graphical displays and calculate summary statistics, probability, confidence intervals, hypothesis testing, regression, and time series analysis.

Topics Statistics has two flavours: first, descriptive statistics, where we summarize observed data; and second, inferential statistics, where we make conclusions about the population the data are drawn from. Probability is the branch of mathematics that describes how samples randomly drawn from a population will behave, and provides the basis for connecting the data and the population from which it is drawn.

Many statistical concepts take time to understand and master. You have probably already met some statistical methods and can calculate averages and draw scatterplots, but you will still need to learn how to interpret them to give information about practical problems and this is best achieved by working through and thinking about a variety of examples. There is nothing special about statistical reasoning. Statistical tools supplement and refine our natural intuition and commonsense. When you are studying, try asking yourself why each conclusion makes sense. You may have to learn some techniques and definitions by rote when you first meet them, but it is useful to look for a pattern. Look back over each completed example to see how the statistical technique has refined your understanding of the problem. This is particularly important if you have a fear of numbers and symbols. Try looking at the problem, the data and the conclusion first, then try to understand how the technique has led from one to the other.

The approach to understanding statistics is no different from any other subject. Plan ahead, work steadily and you can achieve maximum success for your effort. Please contact me if you have any questions about the teaching and learning format for this course.

You don’t need a strong mathematical background to succeed in this course. We teach you to use R to summarize, display and analyse data. We explore data collection techniques including sampling methods and experimental design. We introduce you to probability and statistical inference methods (confidence intervals, hypothesis testing and regression) with an emphasis on communicating results in context. We finish the course with time series analysis and quality management.

We hope you enjoy taking this course as much as we have enjoyed putting it together. We are keen to get feedback from you on things you like as well as anything you don’t like.

We wish you well in your studying.

Syllabus

Course Overview:

This course covers Basic Probability Concepts, Random Variables and Probability Distributions, Sampling Distributions and Basic Statistical Inference, Statistical Modelling, Curve Fitting and Interpolation and Time Series Analysis. Also, we will be introduced R programming language.

Expected outcomes:

Learning outcomes Students who successfully complete this course should be able to:

  • describe the basic concept of probability;

  • apply probability theory to solve real-world problems;

  • use statistical hypotheses for decision-making;

  • develop statistical models to explain a given process;

  • understand the concept of time series;

  • select appropriate time series models for industrial data.

Texts:

  • Introduction to Probability and Statistics for Engineers and Scientists / Sheldon M. Ross— 6th ed. ISBN 978-0-12-824346-6.

  • Probability and Statistics for Engineers and Scientists /Walpole et al. — 9th ed. ISBN 978-0-321-62911-1.

Software:

Evaluation:

The final letter grade for this course will be determined by each method of assessment weighted as follows:

  • In course assessments (50%)
    • Assignment (20%)
    • Mid-semester assessment (30%)
  • End of course examination (50%)

Attendance Policy:

Absence from lectures and/or tutorials shall not exceed \(20\%\). Students exceeding the \(20\%\) limit without an accepted medical or emergency excuse are not permitted to take part in the final examination.