Probability (MAT331) | GSÜ - ECTS Information Guide

Content

Objective

The aim of this course is to learn the definitions, examples and the properties of discrete and continuous random variables and to be able to use them in probability calculations.

Course Content

Combinatorial analysis, Axioms of probability, Conditional probability and independence, Random variables, Continuous random variables, Jointly distributed random variables, Properties of expectation, Limit theorems.

Course Learning Outcomes

To know the definitions , the examples and the properties of discrete and continuous random variables
To be able to calculate the expected value and the standard deviation of the random variables
To be able to use the random variables in the probability calculations.
To understand and to be able to use the limit theorems

Teaching and Learning Methods

Lecture, discussion, problem solving

References

Initiation aux Probabilités, Sheldon Ross

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Permutations and combinations, Sample space and events, Axioms of Probability
2	Conditional probability, Bayes' Formula, Random variables, Discrete random variables
3	Expected Value, Expectation of a Function of a random variable, Variance
4	The Bernoulli and binomial random variables, The Poisson random variable, Other discrete probability distributions
5	Continuous random variables and their expectation and variance
6	The uniform random variable, Normal random variables, Exponential random variables
7	The distribution of a Function of a random variable, Midterm Examination
8	Joint distribution functions, Independent random variables, Sums of independent random variables
9	Conditional Distributions, Joint probability distribution of functions of random variables
10	Properties of expectation, Expectation of sums of random variables, Moments of the number of events that occur
11	Covariance, Variance of sums and Correlations
12	Conditional expectation and prediction, Moment generating Functions
13	Chebyshev’s inequality, The weak law of large numbers,
14	The central limit theorem, The strong law of large numbers

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	1	40
Contribution of in-term studies to overall grade	0	0
Contribution of final exam to overall grade	1	60
Contribution of final exam to overall grade	0	0
Total	2	100

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	0	0
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	0	0
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	0	0
Total	0	0

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways;				X
2	can properly state and use concepts and results of major mathematical interest;				X
3	masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools;				X
4	is able to express one’s mathematical ideas in an organised way both in written and oral forms;		X
5	understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...);			X
6	has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;
8	has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;
9	has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;			X
10	masters French language as well as other foreign languages, to a level sufficient to study or work abroad.			X

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	4	56
Working Hours out of Class	14	4	56
Assignments	4	2	8
Midterm Examinations (including preparation)	1	20	20
Final Examinations (including preparation)	1	30	30
Quiz	2	10	20
Total Workload			190
Total Workload / 25			7.60
Credits ECTS			8