30401  MATHEMATICS AND STATISTICS  MODULE 2 (STATISTICS)
Department of Decision Sciences
OMIROS PAPASPILIOPOULOS
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
 Combinatorics, probability measures and related elementary properties.
 Conditional probability and independence.
 Discrete and continuous random variables. Notable examples. Expected values.
 Joint distribution, independence, correlation, conditional distributions.
 Descriptive statistics, population and sampling, frequency tables, graphs, measures of location and spread.
 Distributions of sampling statistics and related asymptotic distributions.
 Point and interval parameter estimation.
 Hypothesis testing.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
 Understand basic concepts of probability required for the use and interpretation of statistical methods.

Describe a dataset through adequate graphs, tables and statistics.

Identify if the structure of the data allows the application of basic statistical inferential methods.

Do inference on the mean of a population (point estimation/ prediction, interval estimation, hypothesis testing).

Understand the fundamental logic of estimation and hypothesis testing.
APPLYING KNOWLEDGE AND UNDERSTANDING

Understand the challenges derived from the presence of uncertainty in reallife situation.

Choose and apply adequate (basic) statistical tools to aid in the decisionmaking process by learning from available data.

Interpret charts, graphs and statistics and identify possible misrepresentations of data.

Question statements based on data, by analysing the statistical elements and the validity of the assumptions made.
Teaching methods
 Facetoface lectures
 Exercises (exercises, database, software etc.)
 Group assignments
 Interactive class activities (role playing, business game, simulation, online forum, instant polls)
DETAILS
Exercises (Exercises, database, software etc.):
Special sessions with exercises, examples and illustrations of concepts and methods, also with the help of statistical software R, will be provided.
Assessment methods
Continuous assessment  Partial exams  General exam  


x  x 
ATTENDING AND NOT ATTENDING STUDENTS
Students may choose between the following two options:
 Two partial written exams (a midterm and a final) that contribute to the final grade with a 50% weight each.
 A single general written exam (after the end of the course) that counts for 100% of the final mark.
The tests consist of exercises. They aim at ascertaining students' mastery of concepts and results discussed during lectures as well as an adequate knowledge of R.
In each test the maximum grade is 31.
The assessment method is the same for both attending and nonattending students.
Students who take the midterm exam may still take the general exam instead of taking the final exam.
Importantly, access to the final (or second partial) exam follows the rules indicated in Section 7.6 of the Guide to the University.
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
The teaching material will be primarily that developed during the classes and distributed to the students in a PDF format after each class.
The course will use examples and extracts primarily from the first book listed below. It is advisable to acquire this book either in its original publication or its Italian translation (it is also available as an ebook), since it is an excellent modern resource to learn Probability and Statistics and why these are fundamental in anything that has to do with learning from data.
Early chapters from the second book provide an excellent more technical introduction to Probability. The introduction and some Appendices of the third book provide an excellent and accessible introduction to statistical machine learning and the use of Probability and Statistics for designing and analyzing algorithms. The fourth is a textbook whose syllabus correlates highly with the contents of this course. For a number of basic concepts the corresponding Wikipedia pages are a great resource. Please use that instead of random blogs, webpages or videos posted on youtube.

Spiegelhalter, The Art of Statistics: How to Learn from Data, Penguin, 2019, ISBN 9781541618510 (available also in Italian translation)
 Grimmett and Stirzaker, Probability and Random Processes, Oxford, Fourth Edition, 2020, ISBN 9780198847595
 Bishop, Pattern Recognition and Machine Learning, Springer, 2006, ISBN 9780387310732
 S. ROSS, Introduction to Probability and Statistics for Engineers and Scientists, Fourth Edition, Academic Press, 2014