This course is an introduction to modern probability and statistics theory. These are the ones have become essential tools in the modelling and prediction of phenomena aleatory appearing in all fields of engineering.
(+216) 70 014 560
theory of Probabilities
While in theory randomness is an intrinsic property, in practice, randomness is incomplete information . ,Nassim Nicholas Talb.
Content of the module
1. Probabilizes space
(a) Probability (denomination and properties)
(b) Conditional probability
(c) Formula of total probabilities
(d) Bayes formula
(e) Independence
2. Random variables
(a) Real random variables
(b) Distribution function
(c) Law of Probability
(d) Discrete and Continuous Laws
(e) Expectation and variance
(f) Usual laws (Bernouilli, Bin^omial, Fish, Normal and Exponential)
(g) Law of a couple
(h) Covariance
(i) Cauchy-Schwatz inequality
(j) Correlation coecient
(k) Characteristic and generating function
3. Convergences
(a) Near-secure convergence
(b) Convergence in probability
(c) Convergence in law
(d) Markov inequality
(e) I.B.T.
(f) Law of Large Numbers
(g) T.C.L and variants
(h) Examples of approximations of laws