Descriptive Statistics and Introduction to Probability

Abstract

This work is presented as part of the requirements to obtain the University Habilitation, focusing on the subject Descriptive Statistics and Introduction to Probability. It is designed for first-year students in the Preparatory Cycle Department (CP1) at the National Higher School of Mathematics. This course, conducted during the first semester of the academic years 2023– 2024 and 2024–2025, introduces foundational concepts in statistics and probability to build a strong mathematical base for students. The content is structured into three chapters: 1. Fundamentals of Statistics and Numerical Representation of Data: This chapter lays the groundwork by introducing the basic principles of statistics and methods for organizing and representing data numerically and graphically. 2. Two-Way Statistics: Here, the focus shifts to analyzing relationships between two variables using statistical tools such as contingency tables and correlation measures. 3. Introduction to Probability: This chapter provides an entry point into probability theory, covering essential concepts like probability measures, events, and basic properties. 4. Midterm and Final Exam and Solutions The midterm exam and final exam evaluates the knowledge and skills acquired in the course. Below are sample questions along with their solutions: To reinforce the theoretical concepts, each chapter is complemented by a series of exercises with detailed solutions, enabling students to apply and deepen their understanding. Additionally, the course includes a midterm exam and a final exam to assess students’ progress and mastery of the material. v I would like to express my sincere gratitude to Dr. Kessira Abdelrahim for his valuable assistance and support in the preparation of the course material included in this course. His guidance and contributions have been greatly appreciated and have significantly enhanced the quality of the content. vi