De elektronische studiegids voor het academiejaar 2026 - 2027 is onder voorbehoud.





Concepts of Probability and Statistics (9767)
Coordinating lecturer:Prof. dr. Roel BRAEKERS 
Member of the teaching team:Mevrouw Ilaria MISURI 
 Prof. dr. Ivy JANSEN 
 dr. Liz LIMPOCO 
 De heer Pieter GIESEN 

Credits: 6,0
Study load hours: 162
Period: semester 1 (6sp)

Language of instruction: English
Exam contract: not possible

2nd Chance Exam1: Yes
Final grade2: Numerical
Tolerance3: See included in these programmes
Sequentiality
No sequentiality


Prerequisites

The student has a strong knowledge of mathematics.  In the following mathematical topics, the student has a ready knowledge of the calculation techniques:

  • Set theory
  • Functions (univariate and multivariate)
  • Limits and Infinite Sequences
  • Sums and Series
  • Derivatives (univariate and multivariate) and optimization problems
  • Integrals ((In-)Definite and improper integrals, Gamma and Beta functions)


Content

In this course, we deal with the following topics:

Descriptive statistics:
     ·different types of variables
     ·measures of centrality
     ·measures of variability
     ·measures of relative standing
     ·graphical methods to present data

Basic probability theory:
     ·sample space, events, probability, combinatorics
     ·Law of total probability, Bayes rule
     ·stochastic variables, (joint, conditional) distributions, (conditional) expectations
     ·transformation of distributions
     ·Law of large numbers, Central limit theorem
     ·generating samples from a population


Statistical inference:
    ·Confidence intervals: CI for mean(s), CI for proportion(s), CI for variance(s)
    ·hypothesis testing: null-hypothesis, alternative hypothesis, test-statistic, critical value, p-value
        ·hypothesis for mean, proportion and variance
        ·comparing means, proportions, variances                                                                                                                                                                                        Nonparametric ranktests: sign-test, Wilcoxon test and Mann-Whithney test  
    ·Introduction to estimation methods: maximum likelihood, methods of moments, least squares method


Compulsory textbooks (bookshop)
 

Mathematical Statistics and Data Analysis John A. Rice Third Edition Cengage 9780495118688
 

Compulsory course material
 

Lecture notes for the lectures will be provided by the lecturer through the electronic platform
 

Mandatory software
 

R and R-studio


Organisational and teaching methods
Organisational methods  
Collective feedback moment ✔  
Lecture ✔  
Small group session ✔  


Evaluation

Semester 1 (6,00sp)

Evaluation method
Written evaluation during teaching period10 %
Homework✔
Written exam90 %
Open questions✔

Second examination period

Evaluation second examination opportunity different from first examination opprt
No


Learning outcomes
  EC = learning outcomes      DC = partial outcomes      BC = evaluation criteria  
Master of Statistics and Data Science
  •  EC 

    • The student is able to correctly use the theory, either methodologically or in an application context or both, thus contributing to scientific research within the field of statistical science, data science, or within the field of application.

     
  •  DC 

    • The student is able to correctly use the theory in an application context, thus contributing to scientific research within the field of application.

  •  EC 

    • The student is capable of acquiring new knowledge.

 
Included in these programmesTolerance3
N



1   Education, Examination and Legal Position Regulations art.12.2, section 2.
2   Education, Examination and Legal Position Regulations art.15.1, section 3.
3   Education, Examination and Legal Position Regulations art.16.9, section 2.