Probability

This course is designed to familiarize future engineers with the basic concepts of probability calculus and the modeling of random phenomena.
Course outline:


Terminology and notation


Probability space
2.1 Tribe and events
2.2 Probability
2.3 Independence of events
2.4 Conditional probability


Random variables
3.1 Random variable (discrete and density)
3.2 Law of a random variable.
3.3 Expectation of a random variable
3.4 Independence of random variables
3.5 Properties of expectation
3.6 Variance and Covariance
3.7 Tools for random variable laws
3.8 Gaussian vectors


Convergence of random variable sequences
4.1 Different modes of convergence
4.2 Laws of large numbers
4.3 The central limit theorem
4.4 Monte Carlo method

Undergraduate mathematics

Terminology and notation


Probability space
2.1 Tribe and events
2.2 Probability
2.3 Independence of events
2.4 Conditional probability


Random variables
3.1 Random variable (discrete and density)
3.2 Law of a random variable.
3.3 Expectation of a random variable
3.4 Independence of random variables
3.5 Properties of expectation
3.6 Variance and Covariance
3.7 Tools for random variable laws
3.8 Gaussian vectors


Convergence of random variable sequences
4.1 Different modes of convergence
4.2 Laws of large numbers
4.3 The central limit theorem
4.4 Monte Carlo method