A First Course in Probability and Markov Chains (ePub)

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.