A First Course in Probability and Markov Chains

Provides an introduction to basic structures of probabilitywith a view towards applications in information technology A First Course in Probability and Markov Chains presentsan introduction to the basic elements in probability and focuses ontwo main areas. The first part explores notions and structures inprobability, 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 oflarge numbers and central limit theorem. In the second part of thebook, focus is given to Discrete Time Discrete Markov Chains whichis addressed together with an introduction to Poisson processes andContinuous Time Discrete Markov Chains. This book also looks atmaking use of measure theory notations that unify all thepresentation, in particular avoiding the separate treatment ofcontinuous and discrete distributions. A First Course in Probability and Markov Chains: Presents the basic elements of probability. Explores elementary probability with combinatorics, uniformprobability, the inclusion-exclusion principle, independence andconvergence of random variables. Features applications of Law of Large Numbers. Introduces Bernoulli and Poisson processes as well as discreteand continuous time Markov Chains with discrete states. Includes illustrations and examples throughout, along withsolutions to problems featured in this book. The authors present a unified and comprehensive overview ofprobability and Markov Chains aimed at educating engineers workingwith probability and statistics as well as advanced undergraduatestudents in sciences and engineering with a basic background inmathematical analysis and linear algebra.