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## An Introduction to Probability and Stochastic Processes | SpringerLink

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Published 08.01.2019

## Fundamentals of Probability and Stochastic Processes with Applications to Communications

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Along with its Companion Website, the book is suitable as a primary resource for a first course in probability. Moreover, it has sufficient material for a sequel course introducing stochastic processes and stochastic simulation. The flow of the text aids its readability, and the book is indeed a treasure trove of set and solved problems. Every sub-topic within a chapter is supplemented by a comprehensive list of exercises, accompanied frequently by self-quizzes, while each chapter ends with a useful summary and another rich collection of review problems. Because the definitions, theorems, and examples are clearly labeled and easy to find, this book is not only a great course accompaniment, but an invaluable reference. This one- or two-term calculus-based basic probability text is written for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It presents probability in a natural way: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology.

Probability Mass Function & Density Function in Hindi

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time , such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise , or the movement of a gas molecule. They have applications in many disciplines including sciences such as biology , [7] chemistry , [8] ecology , [9] neuroscience , [10] and physics [11] as well as technology and engineering fields such as image processing , signal processing , [12] information theory , [13] computer science , [14] cryptography [15] and telecommunications. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, [a] used by Louis Bachelier to study price changes on the Paris Bourse , [22] and the Poisson process , used by A. Erlang to study the number of phone calls occurring in a certain period of time. The term random function is also used to refer to a stochastic or random process, [26] [27] because a stochastic process can also be interpreted as a random element in a function space.

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