In this book, basic and essential methods for probabilistic and statistical analysis are presented, mainly for university students or other disciplines such as economists, physicists, sociologists, etc. Most of the examples, exercises, and problems are engineering content from the real world, taken from contemporary literature and from my own experience applying probability and statistical methods to engineering problems.

The material focuses more on the methodology of probability and inferential statistics. The necessary mathematical foundations of probability theory and statistics are developed only in essential axioms, theorems, and basic rules. The necessary mathematical proofs are limited to a minimum.

Definitions are emphasized, and in many cases, observations are made to avoid any other misinterpretations in the concepts of probabilities. Additionally, the practical interpretation of many rules or results is given in order for the engineer to understand and use them in their own applications. A particular characteristic of this book is the very good selection of examples, exercises, and problems.

The book includes:

- The basic background of probability theory, for the estimation of the probability of occurrence of stochastic events, such as probability axioms, rules, set operations, combinatorial analysis, conditional probability.

- The basic concepts for random variables, probability distributions, and the necessary assumptions for useful distributions. The most important probability distributions are defined, and their properties related to engineering applications are mentioned.

- The concise presentation of statistical data with frequency tables or histograms and the generalization of sample inferences to the population, such as understanding various estimators and interpreting their basic properties.

- Hypothesis testing, which is very useful in decision making in problems where the reliability of parameter values and their comparison between different populations play a significant role.

- Regression analysis, as most engineering or other scientific problems are directly or indirectly related to some regression model. Regression analysis investigates the possibility of developing reliable prediction models based on the correlation between two or more variables.