Probability

A key pedagogical feature of the textbook is the accessible approach to probability concepts through examples with explanations and problems with solutions. The reader is encouraged to simulate in Matlab random experiments and to explore the theoretical aspects of the probabilistic models behind the studied experiments. By this appropriate balance between simulations and rigorous mathematical approach, the reader can experience the excitement of comprehending basic concepts and can develop the intuitive thinking in solving problems. The current textbook does not contain proofs for the stated theorems, but corresponding references are given.

Moreover, the given Matlab codes and detailed solutions make the textbook accessible to researchers and undergraduate students, by learning various techniques from probability theory and its applications in other fields. This book is intended not only for students of mathematics but also for students of natural sciences, engineering, computer science and for science researchers, who possess the basic knowledge of calculus for the mathematical concepts of the textbook and elementary programming skills for the Matlab simulations.
Contents: PrefaceProbability SpaceRandom Variables and VectorsNumerical Characteristics of Random Variables and VectorsSequences of Random VariablesExamples of Stochastic ProcessesAppendixBibliographyIndex
Readership: Undergraduate and graduate students, professionals and researchers in mathematics, natural sciences, engineering and computer science areas. Probability Concepts;Matlab Simulations;Random Algorithms;Monte Carlo Methods;Stochastic Processes0Key Features:Tight and mathematically exact presentation of probability theory with annotations and explanatory examples. Some of the problems in the textbook involve only mathematical ideas, without Matlab simulations, and some involve bothA variety of exercises with detailed solutions focus on the theory presented through modern applications, such as Bayesian networks, models in population genetics, stochastic processes etc. In addition, there are a variety of tested Matlab codes and simulation examplesWhen reading the textbook, the reader experiences that he is capable of becoming self-absorbed in the field of stochastic and able to solve practical problems by means of simulation models