 671 Introduction to Probability and Statistics

671 Introduction to Probability and Statistics

• Study programme and level: University Study Programme in Administrative Information Science - 1st Cycle
• 1st year
• 6 ECTS
• Course type: Core
• Lectures: 45
• Tutorial: 30
• Other forms of study: 15
• Individual work: 90
• Lecturer: Aleksandar Jurišić, PhD

1. Objectives and competences

• The aim of this course is to introduce students of computer and information sciences to basics of probability theory and statistics.

2. Content

Probability theory, the mathematical description of randomness/uncertainty, is the basis for gambling, insurance and much of modern science.

In statistics »random« is not synonym for »haphazard«. Randomness is kind of order that emerges only in the long run, in many repetitions. We will learn to recognize good and bad methods of producing data. Each set of data contains information about some group of individuals. If we collect data in the form of table, then each row contains data about the corresponding individual and each column contains values of one variable for all individuals.

Statistical tools and ideas assist us to uncover the nature of a set of data using graphs and numbers, which describe main atributes. Such study is called data analysis. We start with one variable and then check relations among several variables.

Statistical inference is a process which infers conclusions based on given data. Informally, statistical inference is often based on graphical presentation of data. Formally, statistical inference uses probability, to judge till what degree are our conclusions reliable, it answers specific questions with a known degree of confidence.

Lectures:

• Definition of probability, algebra of events, conditional probability, Bayes rule, Bernoulli trials, Laplace interval formula, Error function.
• Random variables and vectors, discrete and continuous distributions, independence, functions of random variables, functions of random vectors.
• Expected value, standard deviations and higher moments, sequences of random variables and random processes, limit theorems.
• The main goal of statistics, the sampling distribution of statistics, sample average, reproduction property of the normal distribution, the hi-square distribution, the Student distribution, confidence intervals, estimation, tests of hypotheses, ANOVA, covariance and linear regression.

Tutorials:

• Purpose of tutorials for the course Introduction to Probability and Statistics:
• Detailed study of the material from the lectures through examples.
• Qualitative and quantivative introduction of some typical (real-life) examples that are relevant for students of computer science.
• Tutorials are guided, however, students are independently trying to solve problems, so their presence is compulsory.

Homeworks and quizzes:

• The purpose of homeworks and projects is to offer students a possibility to independent solving of more complex problems in probability and statistics, which assume beside calculation techniques also more comprehensive skills. Both exceeds tutorial work and leads students to independent work. Quizzes encourage students to do current work and give them feedback on their knowledge.

• W. Mendenhall and T. Sincich: Statistics for engineering and the sciences, 5th edition, Pearson-Prentice-Hall, 2007 (prvih 11 poglavij/first 11 chapters).

Dodatna literatura:

• David S. Moore, Part II, Statistics: The Science of Data, v knjigi For All Practical Purposes (Mathematical Literacy in today's world), urednik S. Garfunkel, Consortium for Mathematics and Its Applications (COMAP), 8. izdaja, W. H. Freeman and Company, 2003 (v pripravi je tudi slovenski prevod).
• J. Čibej, Matematika, kombinatorika, verjetnostni račun, statistika, DZS, 1994.
• 3. L. Gonick in W. Smith, The Cartoon guide to Statistics, 1993.

4. Intended learning outcomes

Knowledge and understanding: Student masters the basic techniques to detect relations from data, and ability to use techniques and to evaluate their results.
Application: The ability to detect certain relations from real data.
Reflection: Learning and understanding the soundness between theory and practice applied to specific examples of probability and statistics.

Transferable skills - not related to a single course: This course is a foundation for several courses, where the study and understanding of data patterns allows better decision making and efficient usage of given sources.

5. Learning and teaching methods

Lectures, tutorials, assignments, projects, office hours, lab work. There will be a special emphasis on real-time studies and team work (tutorials and seminars). We will occasionally watch a video material related to the course material.

6. Assessment

• On-going coursework (assignments, midterms, project work) (50%)
• final (written and oral) (50%)