U1.1: Engineering Tools 1
Probability & Statistics
Module designation | Engineering Tools 1 |
Module level, if applicable | 1st year |
Code, if applicable | U1.1 |
Subtitle, if applicable | – |
Courses, if applicable | Probability & Statistics |
Semester (s) in which the module is taught | Semester 1 (S1) |
Person responsible for the module | Dr Issam Khezami |
Lecturer | Afef HIDRI |
Language | French |
Relation to curriculum | Scientific Subject (compulsory), To introduce Probability & Statistics for engineering and application |
Type of teaching, contact hours | 21 hours, of Integrated Course (Classroom Lecture) |
Workload | Total 42Hrs/Semester (21 hours of Self Study) |
Credit points | 1.5 credits |
Requirements according to the examination regulations | – Minimum attendance rate: 80% of the total contact hours >20 % of nonattendance = elimination for exams |
Recommended prerequisites | Basic Mathematics- Probability & Statistics |
Module objectives/intended learning outcomes | Objectives: 1. Introduction of statistics fields of application 2. Understand the technique of programming with R 3. Introduction to Statistics & Probability theory Learning Outcomes: Students will be able to : 1. Learn the main techniques of unvaried and bivariate statistics 2. Implement these techniques appropriately 3. Calculate the probability of random events in daily or professional context. |
Content | Chapter 1 Random experiments 1.1 Random experiment, events, probabilities. 1.2 Independent events. 1.3 Conditional probability, Bayes formula. 1.4 Definition of a Markov chain. Chapter 2 Random variables 2.1 Real random variables. 2.2 Law of probability. 2.3 Distribution function. 2.4 Discrete or continuous variables. 2.5 Density variables. 2.6 Usual laws: Bernoulli’s law, binomial law, geometric law, Poisson law, uniform law, normal law, Cauchy law, exponential law, Chi- Square law. 2.7 Expectation, variance, moments, characteristic function. 2.8 Bienaymé-Chebyshev inequality. Chapter 3 Random vectors 3.1 Independent variables. 3.2 Random vectors: marginal laws, joint law, characteristic function, expectation, covariance matrix. 3.3 Gaussian vectors. 3.4 Conditional expectation. 3.5 Conditional laws. Chapter 4 Convergence theorems for sequences of random variables 4.1 Quadratic mean convergence. 4.2 Law of large numbers. 4.3 Central limit theorem. 4.4 Approximations for binomial laws. |
Study and examination requirements and forms of examination | Format: Written Mid-term Exam (40%) + Final Exam (60%) |
Media employed | Course Material (Hard/ Soft copy) for Classroom & Online (Moodle ULT) |
Reading list | [1] A. Borovkov. Mathematical statistics. Gordon and Breach Science Publishers, 1998. [2] N. Bouleau. Probabilit´es de l’ing´enieur. Variables al´eatoires et simulation. Hermann, 1986. [3] L. Breiman. Probability. Number 7 in Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, 1992. [4] P. Br´emaud. Introduction aux probabilit´es. Springer Verlag, 1984. |