**Quadrimestre 2 - All options**

**48 hours**

**Coordinator : CLG**

**Teaching staff : CLG, BIS, HAL, NRI**

### General course description

After giving the numerous examples of statistics intervening in everyday life, the course presents first the bases of descriptive statistics and second the bases of probability calculation. Descriptive statistics focuses on how observations can be represented (charts or graphs) and how to draw from them characteristic values. The introduction to probability calculation leads to defining a probability and to setting the basic rules for its calculation.

Further to assimilating the bases of descriptive statistics and probability calculus, students are led to discover the main theoretical models of probability distribution which will help them formulate estimates of population averages on the basis of a sample average. The decision making theory is also dealt with.

Some of these techniques will be applied to image processing.

### Learning basic skills

Mathematics course

### Course Aims

The acquisition of basic notions of descriptive statistics and probability calculus.

### Course Outline

#### Chapter 1 : Descriptive statistics

- Introduction
- Observations (charts and graphs)
- Parameters of a one-dimension distribution (position and dispersion: mode, median, quartile, decile, centile, arithmetic mean, variance and standard deviation, coefficient of variation)

#### Chapter 2: Introduction to probability calculus

- Definition of the probability (a posteriori and a priori)
- Theorem of addition (mutually exclusive events)
- Theorem of multiplication (conditional probability and independent events)
- Total probability theorem
- Bayes theorem
- Binomial theorem

#### Chapter 3: Chance variables and probability distribution

- Chance variable
- Probability distribution and distribution function
- Parameters of a probability distribution <1>The main theoretical distributions (binomial, Poison and normal distributions)
- Convergence theorems

#### Chapter 4 : Statistical inference

- Sample theory
- Estimation theory
- Hypothesis test and decision making

### Bibliography

- Course book statistics (1st year)
**J.-J. Droesbeke**, *Eléments de statistique*
- Théorie et applications de la statistique, collection Schaum