Probabilités

Probability

Description: By the end of the core curriculum course in probability, students will have mastered the concepts of random experiments, probability spaces, probability distributions, random variables (RVs), conditioning, and independence of RVs. They will be able to construct an appropriate probability space for a given random experiment (and vice versa), compute and use moments of real or complex RVs, recognize and utilize the Hilbert space structure of second-order complex RVs, and identify and apply various representations of probability distributions (cumulative distribution function, probability density function, characteristic functions, etc.). They will be able to recognize and apply common probability distribution models (Bernoulli, binomial, Poisson, Gaussian, etc.), as well as understand and use the different modes of convergence for sequences of random variables. Finally, they will be able to justify and apply the fundamental theorems of probability theory (Central Limit Theorem, Law of Large Numbers, etc.), and understand and use the concept of conditional expectation.

Learning outcomes: By the end of this course, students will be able to: use the concepts of random experiments, probability spaces, probability distributions, random variables (RVs), conditioning, and independence of RVs; construct an appropriate probability space for a given random experiment and vice versa; compute and use moments of real or complex RVs; recognize and utilize the Hilbert space structure of second-order complex RVs; identify and apply different representations of probability distributions (cumulative distribution function, probability density function, characteristic functions, etc.); identify common probability distribution models (Bernoulli, binomial, Poisson, Gaussian, etc.); recognize and use the different types of convergence for sequences of RVs; justify and apply the fundamental theorems of probability theory (Central Limit Theorem, Law of Large Numbers, etc.); and understand and apply the concept of conditional expectation.

Evaluation methods: 1h30 written test, can be retaken.

Course supervisor: Michel Barret

Geode ID: SPM-MAT-002