Aims

Upon completion of this course, the student is able to

• understand the basic ingredients of probability theory (e.g. sigma-algebra, sample space, probability measure) and to apply the definitions and properties in examples; understand the concepts of independence and conditional probability and to apply them and the laws on conditional probabilities (law of total probability, Bayes' rule) in applications (e.g. system reliability).
• understand, describe, recognize and use several discrete and continuous random variables (both univariate as multivariate); describe and find the univariate and joint distribution of random variables (and transformations of random variables) using probability density functions, cumulative distribution functions and/or moment generating functions.
• calculate and interpret characteristics of random variables (and transformations of random variables): expectations, variances and higher (central) moments directly, by using moment generating functions, by using conditional computing (e.ge. double expectation law) and/or by using the delta method (leading to approximate moments);  calculate and interpret quantiles directly; understand, describe and use the concept of statistical independence (between random variables) and conditional distributions in examples; calculate and interpret covariance and correlation of random variables and moments of order statistics.
• find (sampling) distribution of some common sample statistics and calculate and interpret corresponding moments, probabilities and quantiles; understand, describe and use the concept of convergence (in probability and in distribution) and asymptotic normality of (transformed) random variables and some related properties and theorems (e.g. Chebyshev's inequality, Slutsky's theorem); understand and apply the law of large numbers and the central limit theorem in examples.
• construct point estimators and calculate point estimates (using maximum likelihood method), to evaluate their goodness (calculating bias, variance, mean squared error) and to determine and describe desirable properties of the estimators (related to efficiency, consistency and sufficiency); construct and interpret confidence intervals (and describe and test some of the assumptions that are made).
• describe and perform hypothesis tests, to compute p-values and probabilites of type I and type II errors, to determine the power of a test, to calculate the sample size needed for a given power and to construct likelihood ratio tests and Pearson's chi-squared tests; describe and perform some nonparametric tests; describe the bootstrapping technique and calculating bootstrap estimates of standard error.

Previous knowledge

A practical knowledge of basics of probability, descriptive statistics and applied statistical inference is assumed. The expectation should be to deepen out the foundations and the optimality of methods in statistics, knowing that the mathematical language is a basic tool.


Beginning conditions: Basic calculus (including the concepts of derivative and integration) and a course on statistics, both at undergraduate level.

Order of Enrolment

This course unit is a prerequisite for taking the following course units:
H01F5A : Probabilistisch ontwerpen

Identical courses

This course is identical to the following courses:
G0A17B : Fundamental Concepts of Statistics

Is included in these courses of study

• Doctoral Programme in Business Economics (Leuven)
• Master of Statistics and Data Science (on campus) (Leuven) (European Master of Official Statistics (EMOS)) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Interdisciplinary Statistics and Data Science (No new enrollments for this track as from academic year 2024-2025)) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Statistics and Data Science for Biometrics) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Statistics and Data Science for Business) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Statistics and Data Science for Industry) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Statistics and Data Science for Social, Behavioral and Educational Sciences) 120 ects.
• Master of Statistics and Data Science (on campus) (Leuven) (Theoretical Statistics and Data Science) 120 ects.
• Master of Mathematical Engineering (Leuven) 120 ects.