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Course Syllabus

Bachelor 2020/2021

Probability Theory and Mathematical Statistics

Type: Compulsory course (HSE University and University of London Parallel Degree Programme in Management and Digital Innovation)
Area of studies: Business Informatics
Delivered by: Bachelor's Programme in Digital Product Management
Where: Graduate School of Business
When: 1 year, 4 module
Mode of studies: offline
Open to: students of one campus
Instructors: Margarita Gladkova, Gleb Karpov
Language: English
ECTS credits: 6
Contact hours: 30

Course Syllabus

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Abstract

The main goal of the discipline is to study the basics of probability theory and its applications in management. 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

Learning Objectives

  • be able to summarise the ideas of randomness and variability, and the way in which these link to probability theory
  • have a grounding in probability theory
  • be able to solve typical probabilistic problems
Expected Learning Outcomes

Expected Learning Outcomes

  • 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.
  • Be able to use the concept of conditional probability, law of total probability, notion of independence, collectively exhaustive events.
  • 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.
  • 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.
Course Contents

Course Contents

  • Axioms of probability
    The definition of probability. Interpretations of probability. Counting methods. Combinatorial analysis: permutations, combinations, Partitions, multinomial coefficients. Sampling with and without replacement. Sample space and events. Axioms of probability. Probability as a continuous set function. Venn diagrams.
  • Jointly distributed random variables
    Joint distributions of random variables. Independent random variables. Expected values, covariance. Sums of independent random variables. Conditional distributions. Marginal distributions. Conditional expectation and variance. Joint probability distribution of functions of random variables. Properties of multivariate normal distribution
  • Conditional probability and independence
    Conditional probability. Independent events, mutually exclusive events. Exhaustive events. The law of total probability. Bayes' theorem. Probability trees.
  • Discrete random variables
    Random variables. Discrete and continuous distributions. Cumulative distribution function and its properties. Probability mass function. Common discrete distributions: uniform, binomial, Poisson distributions. Sequences of Bernoulli trials. Expected value, variance and their properties. Functions of a random variable
  • Continuous random variables
    Properties of continuous random variables. Prob- ability density function. Expectation and variance of continuous random variables. Common continuous distributions (uniform, exponential, normal, chi-squared, F-distribution, Student's t- distribution) . The normal approximation of the binomial distribution.
Assessment Elements

Assessment Elements

  • blocking Exam
  • non-blocking Homeworks
  • non-blocking Test
  • non-blocking Quiz
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.5 * Exam + 0.2 * Homeworks + 0.1 * Quiz + 0.2 * Test
Bibliography

Bibliography

Recommended Core Bibliography

  • 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
  • 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
  • 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
  • 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