Probability: an introduction through theory and exercises
This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2023]
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Zusammenfassung: | This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic |
| Beschreibung: | 1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions |
| Beschreibung: | ix, 389 Seiten 611 gr |
| ISBN: | 9783031384912 |
Internformat
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| 500 | |a 1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions | ||
| 520 | |a This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic | ||
| 650 | 4 | |a Measure theory | |
| 650 | 4 | |a Probabilities | |
| 653 | |a Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik | ||
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-38492-9 |
Datensatz im Suchindex
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| id | DE-604.BV049609299 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T23:35:54Z |
| indexdate | 2024-07-20T04:36:19Z |
| institution | BVB |
| isbn | 9783031384912 |
| language | English |
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| physical | ix, 389 Seiten 611 gr |
| publishDate | 2023 |
| publishDateSearch | 2023 |
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| publisher | Springer |
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| spelling | Baldi, Paolo 1948- Verfasser (DE-588)104763130X aut Probability an introduction through theory and exercises Paolo Baldi Cham, Switzerland Springer [2023] ix, 389 Seiten 611 gr txt rdacontent n rdamedia nc rdacarrier Universitext 1 Elements of Measure Theory.- 2 Probability.- 3 Convergence.- 4 Conditioning.- 5 Martingales.- 6 Complements.- 7 Solutions This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.The book begins with a review of the fundamentals of measure theory and integration. Probability measures, random variables, and their laws are introduced next, along with the main analytic tools for their investigation, accompanied by some applications to statistics. Questions of convergence lead to classical results such as the law of large numbers and the central limit theorem with their applications also to statistical analysis and more. Conditioning is the next main topic, followed by a thorough introduction to discrete time martingales. Some attention is given to computer simulation. Through the text, over 150 exercises with full solutions not only reinforce the concepts presented, but also provide students with opportunities to develop their problem-solving skills, and make this textbook suitable for guided self-study.Based on years of teaching experience, the author's expertise will be evident in the clear presentation of material and the carefully chosen exercises. Assuming familiarity with measure and integration theory as well as elementary notions of probability, the book is specifically designed for teaching in parallel with a first course in measure theory. An invaluable resource for both instructors and students alike, it offers ideal preparation for further courses in statistics or probability, such as stochastic calculus, as covered in the author's book on the topic Measure theory Probabilities Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik Erscheint auch als Online-Ausgabe 978-3-031-38492-9 |
| spellingShingle | Baldi, Paolo 1948- Probability an introduction through theory and exercises Measure theory Probabilities |
| title | Probability an introduction through theory and exercises |
| title_auth | Probability an introduction through theory and exercises |
| title_exact_search | Probability an introduction through theory and exercises |
| title_exact_search_txtP | Probability an introduction through theory and exercises |
| title_full | Probability an introduction through theory and exercises Paolo Baldi |
| title_fullStr | Probability an introduction through theory and exercises Paolo Baldi |
| title_full_unstemmed | Probability an introduction through theory and exercises Paolo Baldi |
| title_short | Probability |
| title_sort | probability an introduction through theory and exercises |
| title_sub | an introduction through theory and exercises |
| topic | Measure theory Probabilities |
| topic_facet | Measure theory Probabilities |
| work_keys_str_mv | AT baldipaolo probabilityanintroductionthroughtheoryandexercises |