This concise textbook covers the full scope of an introductory course in modern probability theory, from elementary combinatorial methods to the central limit theorem, while maintaining mathematical rigor. It includes key topics like the measure extension and the Radon-Nikodym theorems. Designed for a one-semester course, it is well-suited for theoretical mathematics, financial mathematics, insurance, or stochastic modeling students. With 375 exercises, it offers ample opportunities for study and review.
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1. The Beginning.-
2. The General Definition of Probability.-
3.
Random Variables and Their Distributions.-
4. Expected Value for Random
Variables.-
5. Random Variable Parameters.-
6. Characteristic Functions.-
7.
Limit Theorems.-
8. Extension of Measure.
Jolanta Misiewicz studied at Wrocaw Technical University, Poland, where she received a PhD in 1981 and a Habilitation in 1997. In 2007, she received the title of Professor from the President of Poland. Her scientific specialty is analytical methods in probability and stochastic processes. She is the author of over 50 journal articles and co-author of two monographs. She has held positions at Wrocaw Technical University, the University of Zielona Góra, and Warsaw Technical University, where she is now Professor Emeritus.
