This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of probability theory to the asymptotics of independent random sequences and an introduction to inferential statistics. The necessary basics on measure theory are included to ensure the book is self-contained. Illustrations are provided from many applied fields, including information theory and reliability theory. Numerous examples and exercises in each chapter, all with solutions, add to the main content of the book.
Written in an accessible yet rigorous style, the book is addressed to advanced undergraduate students in mathematics and graduate students in applied mathematics and statistics. It will also appeal to students and researchers in other disciplines, including computer science, engineering, biology, physics and economics, who are interested in a pragmatic introduction to the probability modeling of random phenomena.
- 1. Events and Probability Spaces. - 2. Random Variables. - 3. Random
Vectors. - 4. Random Sequences. - 5. Introduction to Statistics.
Valérie Girardin is an Exceptional Class Associate Professor at the CNRS Laboratory of Mathematics Nicolas Oresme (LMNO), Université de Caen Normandie, France. Agrégée in mathematics, she also holds the French Habilitation, a requirement to supervise PhD students. She teaches analysis, probability and statistics to various types of students, including future secondary school teachers in mathematics. Her research interests include diverse aspects of stochastic processes, from theory to applied statistics, with a focus on entropy. Nikolaos Limnios is a Full Professor at the Applied Mathematics Laboratory (LMAC) at the Université de Technologie de Compiègne (UTC), France. He teaches probability, statistics and stochastic processes to future engineers. His research interests in probability and statistics include Markov, semi-Markov processes, random evolutions, and their applications.
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