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Probability and Statistics: Theory and Exercises

  • Book

  • March 2024
  • Bentham Science Publishers Ltd
  • ID: 5960309
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

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: PROBABILITIES

CHAPTER 1 REMINDER ON THE THEORY OF SETS
  • INTRODUCTION
  • DEFINITION
  • Cardinality of a Set
  • VENN Diagram
  • Subsets
  • Main Properties of Sets
  • The Tribe
CHAPTER 2 INTRODUCTION TO BASIC DEFINITIONS IN PROBABILITY
  • INTRODUCTION
  • RANDOM EXPERIMENT (RE)
  • Events
  • DEFINITION OF A PROBABILITY
CHAPTER 3 COMBINATORY ANALYSIS
  • INTRODUCTION
  • MULTIPLICATION PRINCIPLE (GENERAL PRINCIPLE OF
  • ENUMERATION)
  • PERMUTATIONS
  • Permutation without Repetition
  • ARRANGEMENTS
  • Arrangement without Replacement
  • Arrangement with Replacement
  • COMBINATIONS
CHAPTER 4 CALCULATION OF PROBABILITIES
  • 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
CHAPTER 5 RANDOM VARIABLE
  • 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
CHAPTER 6 DISTRIBUTION LAWS
  • INTRODUCTION
  • DISTRIBUTION FUNCTION (CUMULATIVE DISTRIBUTION
  • FUNCTION (CDF))
  • Discrete Random Variable
  • Binomial Law
  • Other laws of Distribution
  • CENTRAL LIMIT THEOREM
PART 2: STATISTICS

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