UCL - Mathematics for the statistician - Introduction to probability and statistics.

[STAT2010]

[30h + 45h] 10 credits

This course is taught in the 1st semester.

Teacher(s): Johan Segers, Ingrid Van Keilegom

Language: French

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

By the end of the course, the student will be familiar with the basis of mathematics, probability and statistics, necessary to start the courses of methodology and practice of statistics of the program.

Main themes

PART I : Mathematics :
Analysis of functions, limits, continuity, derivatives, integrals, matrix algebra.

Part II : Probability :
Event, probability and conditional probability, Bayes theorem, discrete and continuous random variables, particular laws, density function, distribution function, moments, random vector, limit theorems.

PART III : Statistics :
Point estimation, confidence interval and hypothesis testing with application to the case of normal population(s) or proportions.

Content and teaching methods

Content
PART I : Mathematics :
Analysis of functions, limits, continuity, derivatives, integrals, matrix algebra.

Part II : Probability :
Event, probability and conditional probability, Bayes theorem, discrete and continuous random variables, particular laws, density function, distribution function, moments, random vector, limit theorems.

PART III : Statistics :
Point estimation, confidence interval and hypothesis testing with application to the case of normal population(s) or proportions.

Teaching methods
The course consists of lectures and exercise sessions.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Evaluation
The evaluation consists of a written exam.
Teaching materials
The course notes will be distributed during the first lecture of the course.

Others
Professors :
- Johan Segers, phone : 010/47 43 11, e-mail : lambert@stat.ucl.ac.be
- Ingrid Van Keilegom, phone : 010/47 43 30, e-mail : vankeilegom@stat.ucl.ac.be

References :
Dowling, E.T. (1995), Mathématique pour l'économiste, McGraw-Hill, London.
Droesbeke, J.-J. (1997). Eléments de Statistique. Editions de l'Université de Bruxelles & Editions Ellipses.
Khuri, A (1993), Advanced calculus with applications in statistics, Wiley, New York.
Wackerly D.D., Mendenhall W. and R.L. Scheaffer 5th Ed (1996) Mathematical Statistics with Applications, ITP, Duxbury Pres