Probability and Statistics: Theory and Exercises is a textbook focused on practical examples of probability theory and statistics, with the goal of giving readers a thorough understanding of mathematical relationships in these subjects. The book is designed for basic courses in probability and statistics, and is aimed primarily at non-specialists and beginner level students.
The book is divided into 2 sections, respectively.
Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws
Statistics: Covers basic concepts of descriptive statistics
The book is divided into 2 sections, respectively.
Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws
Statistics: Covers basic concepts of descriptive statistics
Key Features
- Simple, clear language for easy comprehension of key concepts
- Carefully chosen exercises with solutions for self-learning
- Over 40 Illustrations for clear explanations
- References for further reading and tutorials
Readership
Beginner-level students and non-experts.Table of Contents
PART 1: PROBABILITIESCHAPTER 1 REMINDER ON THE THEORY OF SETS
- INTRODUCTION
- DEFINITION
- Cardinality of a Set
- VENN Diagram
- Subsets
- Main Properties of Sets
- The Tribe
- INTRODUCTION
- RANDOM EXPERIMENT (RE)
- Events
- DEFINITION OF A PROBABILITY
- INTRODUCTION
- MULTIPLICATION PRINCIPLE (GENERAL PRINCIPLE OF
- ENUMERATION)
- PERMUTATIONS
- Permutation without Repetition
- ARRANGEMENTS
- Arrangement without Replacement
- Arrangement with Replacement
- COMBINATIONS
- INTRODUCTION
- PROBABILITY TREE
- Compatible Events
- Incompatible Events
- CALCULATION RULE
- TOTAL PROBABILITY LAW
- CONDITIONAL PROBABILITY
- TREE DIAGRAM OF PROBABILITIES IN THE GENERAL CASE (TWO
- RANDOM SUB-EXPERIMENTS)
- GLOBAL (OVERALL) PROBABILITY
- BAYES’ THEOREM
- INTRODUCTION
- RANDOM VARIABLE DEFINITION
- Sets Defined Using x
- MATHEMATICAL EXPECTATION (EXPECTED VALUE)
- VARIANCE AND STANDARD DEVIATION
- QUANTITATIVE AND QUALITATIVE RANDOM VARIABLES
- Bernoulli’s Random Variable
- Types of Random Variables
- INTRODUCTION
- DISTRIBUTION FUNCTION (CUMULATIVE DISTRIBUTION
- FUNCTION (CDF))
- Discrete Random Variable
- Binomial Law
- Other laws of Distribution
- CENTRAL LIMIT THEOREM
CHAPTER 7 DEFINITIONS AND CALCULATIONS IN STATISTICS
- INTRODUCTION
- SOME VOCABULARIES
- Population
- Individual
- Sample
- Modality
- A STATISTICAL SERIES (WITH ONE VARIABLE) {(xi ,ni )}
- Graphical Representation
- THE CENTRAL TENDENCY OF A STATISTICAL SERIES AND ITS
- INDICATORS
- The Mode
- The Median
- STATISTICAL SERIES FORMED ACCORDING TO THE VALUES OF
- CENTRAL TENDENCY INDICATORS
- OTHER TYPES OF THE MEAN
- The Harmonic Mean
- The Geometric Mean
- The Extent
- STANDARD DEVIATION
- CONFIDENCE INTERVAL
- Risk of Error
- SERIES OF PROBABILITY EXERCISES
- SERIES OF STATISTICS EXERCISES
- SERIES CORRECTION PROBABILITIES
- SERIES CORRECTION STATISTICS
- CONCLUSION
- REFERENCES
- SUBJECT INDEX
Author
- Horimek Abderrahmane
