Probability and statistics

Reminders and introductions to probability theory and its applications in statistics.
Contents:
Counts. Definitions (universe, event, probabilities... Discrete and continuous random variables...). Bernoulli, binomial, Poisson, Normal laws...
Some notions of descriptive and theoretical statistics (confidence intervals...).

1) Probability theory.
- Counts.
- Definitions: event, its probability...
- Discrete and continuous random variables: properties, distribution function, density, characteristic and generating functions.
- Pair of v.a.: covariance, correlation
-Tchebicheff and limit theorems.
- Case studies: Bernoulli's law, binomial, Poisson, Normal...
- Notion on random functions.
2) Statistics
- Elements of descriptive statistics (Use of Excel)
- Elements of theoretical statistics: estimator, estimation, confidence interval, test of conformity of a theoretical law to an experimental distribution, Chi-square test.