Semestre 3

Course : Probability and Statistics 2
Level : 2nd Years State Engineer in Computer Science
Instructor : Dr. Ahmed Bouchenak (Associate Professor -
Email : a.bouchenak@univ-mascara.dz
Teaching unit : Methodological
Credits : 3
Coe?cient : 2
Hourly volumes (per week) : Course (1h30) TD (1h30)

Course goals : The objective of this course is to :
- Allow the student to be well equipped to approach other concepts and themes of probability
and statistics in more depth.
- Introduction to inductive statistics which, thanks to the assimilation of experimental obser-
vations to theoretical laws and the application of tests, provides decision-making elements.
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Course topics :
Chapter 1 : Modes of Convergence
1- Convergence in Probability (The Weak Law of Large Numbers).
2- Convergence with Probability 1 (The Strong Law of Large Numbers).
3- Convergence in Distribution.
4- The Central Limit Theorem.
Chapter 2 : Statistical Inference
1- Hypothesis Testing.
2- The Chi-Square Test.
3- Point of Estimation and Con?dence Interval Methods.
Chapter 3 : Some Selected Themes of Probability
1- Poisson Process.
2- Statistical Survey.
3- Survey Techniques.
4- Waiting Lines.
Chapter 4 : Markov Chains
1- Examples of Markov Chains.
2- Computing with Markov Chains.
3- Stationary Distribution.
4- Markov Chain Limit Theorem.
5. Markov Process.

References :
1. J. Fourastie, B. Sahler : Probabilités et statistique, Série J Quinet, édition Dunod 1981.
2. C. Leboeuf, J.L.Roque, J.Guegand : cours de probabilités et statistiques, ellipses-marketing
1983.
3. J.Genet, G.Pupion, M.Repussard : probabilités, stastiques et sondages. Vuibert 1974.