Provides an introduction to basic structures of probability with a
view towards applications in information technology
A First Course in Probability and Markov Chains presents an
introduction to the basic elements in probability and focuses on two
main areas. The first part explores notions and structures in
probability, including combinatorics, probability measures, probability
distributions, conditional probability, inclusion-exclusion formulas,
random variables, dispersion indexes, independent random variables as
well as weak and strong laws of large numbers and central limit theorem.
In the second part of the book, focus is given to Discrete Time Discrete
Markov Chains which is addressed together with an introduction to
Poisson processes and Continuous Time Discrete Markov Chains. This book
also looks at making use of measure theory notations that unify all the
presentation, in particular avoiding the separate treatment of
continuous and discrete distributions.
A First Course in Probability and Markov Chains:
- Presents the basic elements of probability.
- Explores elementary probability with combinatorics, uniform
probability, the inclusion-exclusion principle, independence and
convergence of random variables.
- Features applications of Law of Large Numbers.
- Introduces Bernoulli and Poisson processes as well as discrete and
continuous time Markov Chains with discrete states.
- Includes illustrations and examples throughout, along with solutions
to problems featured in this book.
The authors present a unified and comprehensive overview of probability
and Markov Chains aimed at educating engineers working with probability
and statistics as well as advanced undergraduate students in sciences
and engineering with a basic background in mathematical analysis and
linear algebra.
