Theory Probability

Course unit code

Specialization:

02.03.02 Computer science and information technologies, 02.03.03 Mathematical support and information systems administration, 09.03.03 Applied computer science, 09.03.04 Software Engineering

Course unit title

Theory Probability

Name(s), surname(s) and title of lecturer(s)

Anna V. Kitaeva, professor

Level of course

Bachelor

Semester

3 or 4

ECTS credits

3

Working hours

Contact hours

58

lectures

30

seminars

practical classes

28

laboratory classes

consultations

4

Independent work

44

Total

106

Work placement

none

Language of instruction

English

Prerequisites

Calculus, Linear algebra

Objectives of the course

Learning outcomes

A student’s assessments methods

The key aim has been to develop the ability to construct probabilistic models in a manner that combines intuitive understanding and mathematical precision.

While mastering the discipline the following expertise is evolved in students:

а) general: to analyze and generalize the information; to express the thoughts clearly.

b) professional: to use probabilistic methods in their professional activity; to choose methods for solving management and design tasks in the sphere of computer science and technology; to justify the decisions, to prove their correctness.

As a result a student should:

Know: the basic concepts and models of modern Probability: probability space, random event, random variable, distribution, independence, sample space; the basic methods of probability calculation: combinatorics, conditioning, sum and product rules; basic discreet and continuous distributions, their properties and the field of application.

Be able to: apply probabilistic methods to solve various theoretical and practical tasks; calculate the probabilities of compound events; find numerical characteristics of random variables.

Have skills of: elementary probability calculation.

work with the course book, research and review of literature and other electronic sources on a given problem individually, homework, home tests, advanced self-study, self-study of a particular subject, tests, exersises, tests and exam.

Teaching methods

Lectures, solving exercises, independent study of literature and other electronic sources, case studies, testing.

Course unit content

Title

Lectures  (hours)

Self-study (hours)

Practice

(hours)

1. Basic probability concepts

3

2

2 

2. Combinatorics

2

6

3 

3. Properties of probability

2

6

2 

4. Conditional probability. Independence

2

6

4 

5. The Monty Hall problem and other puzzles

2

6

3 

6. Discrete random variables

7

6

5 

7. Continuous random variables (RVs with densities)

7

6

5 

8. Limit results for sequences of random variables

5

6

4

30

44

28

Assessment requirements

Student’s skills in this subject will be evaluated by means of discussions at the seminars, solving tasks, writing tests and final examination.

Assessment criteria

The assessment is carried out by the following criteria: clarity of explanation; logical thinking; achiving the specified learning standards (some percentages of the tests' performance, solved exercises).

The composition of final accumulative mark

Final accumulative mark consists of: 4 tests –10% each, exam –  60%

Course outline arranged by