Probabilités et statistique [INFOB223]

At the end of this lecture, a student should be able 

• to manage a statistical analysis of a given set of data,
• to realize a statistical test, and accordingly to interpret the hidden meaning of their data, 
• to use R language, 
• to use combinatorial calculus and probability calculus to compute probabilities of complex events, 
• to use fonctional analysis, linear algebra, and discrete mathematics to compute laws of probability of complex random phenomena, 
• to use basic probability laws to explain random phenomena, 
• to use probability theory to examine joint random variables. 

The student's objectif is to deeply understand the probability theory and statistical theory, and the related technics. On purpose we simplify the mathematical formalism to better highlight the intuition behind probability theory. We use measure theory to extend the descriptive analysis methods to probability theory (random variables).

We start with descriptive statistics, followed by probability theory basics (random variable, common law of probability,...) We use R for analysis of sets of data. We use probability theory to introduce the intuition behind inferential statistics (confidence interval and tests).