Bachelor
2022/2023

# Probability Theory and Mathematical Statistics

Type:
Compulsory course (Management and Digital Innovation)

Area of studies:
Business Informatics

Delivered by:
Department of Business Informatics

Where:
Graduate School of Business

When:
1 year, 4 module

Mode of studies:
offline

Open to:
students of one campus

Language:
English

ECTS credits:
3

Contact hours:
48

### Course Syllabus

#### Abstract

This is second half of the course Probability Theory and Mathematical Statistics which is a core mathematical subject and is dedicated to statistical part of the course. The statistical section starts with the descriptive techniques but quickly switches to the inferential methods. The topics covered here include sampling distributions, point and interval estimates, hypothesis testing. We conclude with a univariate and, if time permits, multivariate regression. This course is the basis for the development of students' skills in probabilistic and statistical thinking, needed for analysis and modeling in management.

#### Learning Objectives

- be able to summarise the ideas of randomness and variability, and the way in which these link to probability theory
- • Be able to process the empirical data; .
- have a grounding in probability theory
- • Be able to apply statistical methods to solve applied managerial problems;
- be able to solve typical probabilistic problems
- • Be familiar with Microsoft Office programs for empirical data processing

#### Expected Learning Outcomes

- Be able to build, assess the quality and make predictions with the linear regression model.
- Be able to derive and use the main sampling distributions - for mean, proportion and variance
- Be able to estimate the main characteristics of a random variable by means of point or interval estimates. Know how to construct and interpret the confidence intervals for mean, proportion and variance.
- Be able to use the concept of conditional probability, law of total probability, notion of independence, collectively exhaustive events.
- Be able to use the methods of descriptive statistics to summarize and visualize the raw data.
- Be aware of different definitions of probability, the axioms of probability and their use for derivation of major probabilistic relationships. Know the basic counting methods and principles of combinatorics.
- Know and be able to use alternative ways of describing a continuous random variable - probability density function and cumulative distribution function. Know how to calculate basic characteristics of a continuous random variable. Be aware of commonly used continuous distributions.
- Know how to work with a multivariate random variable using the joint probability distribution. Be able to detect the indepedent random variables, calculate the marginal and conditional distributions, covariance and correlation between the variables.
- Understand the principles of hypothesis testing. Be able to perform tests for population mean, proportion and variance.
- Understand what is meant by a random variable. Know how to use the probability mass functions for calculating the basic characteristics of a discrete random variable (expected value, variance). Be aware of commonly used discrete distributions.

#### Course Contents

- Axioms of probability
- Jointly distributed random variables
- Probability Theory Revision: Random Variables
- Conditional probability and independence
- Discrete random variables
- Ideas of sampling and sampling distributions
- Continuous random variables
- Methods of descriptive statistics
- Point and interval estimates
- Hypothesis testing
- Linear regression model

#### Interim Assessment

- 2022/2023 4th module0.1 * Quiz + 0.5 * Exam + 0.25 * Homeworks + 0.15 * Test
- 2023/2024 1st module0.3 * Home assignments + 0.4 * Exam + 0.2 * In-class tests + 0.1 * Quiz

#### Bibliography

#### Recommended Core Bibliography

- Biswas, D. (2019). Probability and Statistics: Volume I. [N.p.]: New Central Book Agency. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2239779
- Blitzstein, J. K., & Hwang, J. (2019). Introduction to Probability, Second Edition (Vol. Second edition). Boca Raton, FL: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=2024519

#### Recommended Additional Bibliography

- Balakrishnan, N., Koutras, M. V., & Konstantinos, P. (2019). Introduction to Probability : Models and Applications. Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2097342
- Ghahramani, S. (2018). Fundamentals of Probability : With Stochastic Processes (Vol. Fourth edition). Boca Raton, FL: Chapman and Hall/CRC. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1875108
- Linde, W. (2017). Probability Theory : A First Course in Probability Theory and Statistics. [N.p.]: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1438416
- Linton, O. B. (2017). Probability, Statistics and Econometrics. London, United Kingdom: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1200673