Mathematical Statistics for International Business (2016/17)



The main focus of this course is to develop skills helpful in decision making towards uncertainty.The course provides the students with the understanding of probability, theory of estimation, and hypothesis testing.


Mathematics, statistics, microeconomics, macroeconomics.


Some Helpful Files: course outline, description of homework assignments, grading scale matrix
download files in .rar-format

Quantitative Methods: introduction with examples and exercises
download files in .rar-format


Mendenhall, W., Scheaffer, R. L., Wackerly, D. D. (1981), Mathematical Statistics with Applications, 2nd. edition, Duxbury Press, Boston

Anderson, D.R., Sweeney, D.J., Williams, T.A. (2007), Statistics for Business and Economics, West Publishing Company, Minneapolis/St. Paul, New York, Los Angeles, San Francisco.

Bickel, P. J., Doksum, K. A. (1977), Mathematical Statistics. Basic Ideas and Selected Topics, Holden-Day, Inc., San Fransisco.

Koralov, L. B., Sinai, Y. G. (2007), Theory of Probability and Random Processes 2nd. edition, Springer-Verlag, Berlin, Heidelberg.


download for Windows useres
download for Mac useres

manuals and hints

Assessment and Student Evaluation

Research Project (40%):

You are going to prepare, present, and defend a written research project based on the procedures presented throughout the course. To improve your team work ability the projects as well as the homework assignments could be prepared in groups (max. of 4 persons).

Homework Assignments (15%):

Homework assignments should be submitted as an e-mail attachment (preferably in .pdf or .docx format) prior to the next class.

Midterm Examinations (20%):

1. Week 4 – Probability;
2. Week 6 – Probability distributions, moments;
3. Week 10 – Estimation and Hypothesis Testing;

Final Examination (25%):

There will be a writen examination at the end of the course.

Grading Scale

Lecture and Laboratories:

A (6) 90-100 %
B (5) 80-89 %
C (4) 70-79 %
D (3+) 60-69 %
E (3) 51-59 %
F (2) below 50 %
(Polish equivalent in parentheses)

Course Outline

Block 1: Introduction

Activity: sets, matrix algebra, integrals;

Eigenmath Files: matrix multiplication; definite integral;

Presentation: descriptive statistics
download file

Presentation: introduction to calculus and linear algebra
download file

Exercise: descriptive statistics and discountng policy of Wernham Hogg's branches
download file

R Script: Descriptive statistics in R

R Script for Homework Assignment 27.11.: Her Majesty the Queen
interpret graphs and results

Presentation: download file in .rar-format

Block 2: Probability

Activity: sample space, probability measure, axiomatic definition of probability;

Presentation: sample space, sigma-algebra, probability
download file

Exercises and Presentation: unconditional probability, some helpful counting rules
download file

Chapter: sample space, sigma-algebra, probability
download file

Block 3: Conditional Probability

Activity: conditional probability, independence, Bayes’s rule;

Presentation: contingency table, frequency table, Venn diagrams
download file

Excel File + Description: download files in .rar-format

R Script: contingency and frequency tables in R *

Exercise: Sherlock Holmes: A Game of Shadows
download file

Exercise: NBP, interest rate, and inflation
download file

* R: An IntRoduction an R-script for contingency and frequency tables

Block 4: Central Moments

Midterm Examination: Probability.

Activity: expected value, variance, conditional moments, Chebyshev's inequality;

Exercise: Bond. James Bond
download file

Presentation: Chebyshev Inequality
download file

Exercise: Chebyshev Inequality

Block 5: Distribution and Density Functions

Activity: (week 1) histogram, kernel distribution, calculating probability by using distribution function, normal distribution, Gamma distribution, Beta distribution

Activity: (week 2) Gamma-family distributions, fitting distributions to data

Presentation: CDF and PDF
download file

Data: Federal Reserve Bank of New York survey data on expectations

R Script: histogram and kernel distribution in R

Exercise: Using approximated function to calculate probability

Exercise: R script

Presentation: Common Probability Distributions
download file

R Script: Normal, Gamma, and Beta distributions in R

Presentation: Common Probability Distributions: Moments
download file

Exercise: Probability distributions and their moments

R Script: Fitting theoretical distribution to empirical distribution in R

Block 6: Sampling Distribution

Activity: statistic, sampling distribution, Central Limit Theorem

R Script: sampling distribution in R

Block 7: Hypothesis Testing

Activity: null hypothesis, alternative hypothesis, significance level, p-value, selected testing procedures

R Script: hypothesis testing in R

Data and Exercises: Redskins' Payroll 2015: hypothesis testing;