This book introduces students to probability, statistics, and stochastic processes. It can be used by both students and practitioners in. Introduction to Probability, Statistics, and Random Processes is an open access peer-reviewed textbook intended for undergraduate as well as first-year. Introduction to Probability, Statistics and Random Processes Link: HTML and PDF files with commentary at tvnovellas.info Stable link here.
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Online textbook -> Exam-friendly, offline, searchable PDF - casrou/ProbToPdf. ProbToPdf/Introduction to Probability, Statistics, and Random Processes. Introduction to Probability, Statistics, and Random Processes Hardcover pages; eBook HTML and PDF Files; Language: English; ISBN/ASIN. Welcome. This site is the homepage of the textbook Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik. It is an open access.
About this book An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena. Additional topical coverage includes: Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.
So the natural question you might ask is, why are we doing this?
What's so useful about defining random variables like this? It will become more apparent as we get a little bit deeper in probability. But the simple way of thinking about it is as soon as you quantify outcomes, you can start to do a little bit more math on the outcomes. And you can start to use a little bit more mathematical notation on the outcome. So for example, if you cared about the probability that the sum of the upward faces after rolling seven dice-- if you cared about the probability that that sum is less than or equal to 30, the old way that you would have to have written it is the probability that the sum of-- and you would have to write all of what I just wrote here-- is less than or equal to You would have had to write that big thing.
And then you would try to figure it out somehow if you had some information. But now we can just write the probability that capital Y is less than or equal to It's a little bit cleaner notation.
And if someone else cares about the probability that this sum of the upward face after rolling seven dice-- if they say, hey, what's the probability that that's even, instead of having to write all that over, they can say, well, what's the probability that Y is even? Now the one thing that I do want to emphasize is how these are different than traditional variables, traditional variables that you see in your algebra class like x plus 5 is equal to 6, usually denoted by lowercase variables.
These variables, you can essentially assign values.
You either can solve for them-- so in this case, x is an unknown. You could subtract 5 from both sides and solve for x. Say that x is going to be equal to 1. In this case, you could say, well, x is going to vary. We can assign a value to x and see how y varies as a function of x.
You can either assign a variable, you can assign values to them. Or you can solve for them. You could say, hey x is going to be 1 in this case.
That's not going to be the case with a random variable. A random variable can take on many, many, many, many, many, many different values with different probabilities. And it makes much more sense to talk about the probability of a random variable equaling a value, or the probability that it is less than or greater than something, or the probability that it has some property.
And you see that in either of these cases.
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Book Description This book introduces students to probability, statistics, and stochastic processes. Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods Single and multiple random variables discrete, continuous, and mixed , as well as moment-generating functions, characteristic functions, random vectors, and inequalities Limit theorems and convergence Introduction to Bayesian and classical statistics Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion Simulation using MATLAB and R online chapters The book contains a large number of solved exercises.
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