Aims

To lay down the fundamentals of statistical data analysis in the natural sciences, and of statistical inference.
The student is initiated to the theory of probability, the concept of random variable, the principal models of discrete and continuous random variables. He understands the role of sampling and the principles of statistical inference, and applies these to some simple problems.
After completing this course, the student should be able to fruitfully take courses on the application of methods of data analysis and of statistical inference to the various fields of natural sciences.

Main themes

1) Introduction to probability theory and practice.
2) Random variables : concept, types (discrete, continuous, uni- or multivariate), properties of random variables and of functions thereof, principal models.
3) Introduction to statistical inference : theory, applications.
The practicals help the student in testing his understanding of the concepts, his ability to apply them, and in revising the techniques of descriptive statistics.

Content and teaching methods

1) Introduction : What is statistics ? What is its usefulness in the natural sciences ? Aims of the lecture, means, support, evaluation.
2) Introduction to probability theory : Random experiment, events, axioms of probability, probability and frequency, joint, marginal, conditional, total, composed probabilities, Bayes formula, independence. Illustrations.
3) Random variables : concept, types, properties, functions of random variables, principal probability models of discrete and of continuous variables, introduction to two-dimensional variables, covariance and correlation.
4) Principles of statistical inference : Population and sample, sampling, statistics, sampling distribution, qualities of an estimator, estimation methods, point and interval estimation, hypothesis testing, error risks, power of a test.
5) Introduction to the inference concerning averages : one, two, or several populations (using the Normal or the Student laws or the analysis of variance).
The presentations rely heavily upon illustrations. The practicals are essential to a good understanding and mastering of the concepts.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

PREREQUISITE
Basic notions of calculus; elements of set theory and of linear algebra
EVALUATION
Written examination evaluating mainly the understanding and capacity to apply the concepts and reasoning. The student is allowed to use the official booklet of formulae, of statistical tables, and a hand-calculator.
SUPPORT
Syllabus, booklet of exercises, of formulae, of statistical tables. Overheads. This course is on iCampus, where more information is available and the yearly calendar of activities is posted.

Other credits in programs