Mathematical Statistics

Advanced Set Theory

In Advanced Set Theory, we study many important ideas related to the size and structure of sets. We begin by discussing equivalent sets and understanding the difference between countable and uncountable sets, along with their examples. We explore cardinal numbers as a way to compare set sizes and learn about Cantor’s theorem which shows that some infinities are bigger than others. We also look at partially ordered sets, chains, and lattices, which help us understand the order and arrangement of elements. The Cantor-Bernstein theorem helps in proving when two sets have the same size. We learn how to add, multiply, and take powers of cardinal numbers. Important logical tools like the Axiom of Choice and Zorn’s Lemma are also studied, along with their equivalence. Finally, we discuss well-ordered sets, ordinal numbers, and how we can perform addition and multiplication with them. All these concepts help us deeply understand infinite sets and the foundations of modern mathematics. Notes ●...

Mathematical Statistics

Mathematical Statistics is a branch of mathematics that deals with the theoretical foundation of statistical methods. It involves the study of probability theory, random variables, probability distributions, expectation, variance, and statistical inference. In this field, concepts such as estimation, hypothesis testing, confidence intervals, and regression analysis are rigorously developed and analyzed. Mathematical statistics provides the tools needed to make reliable decisions based on data, especially in situations involving uncertainty. It plays a crucial role in various disciplines, including economics, biology, engineering, and social sciences, where accurate data analysis and interpretation are essential.

Notes

Books

📗 Introduction to Statistical Theory
Part - I by Sher Muhammad Chuhdary
Click here to download
📗 Introduction to Statistical Theory
Part - II by Sher Muhammad Chuhdary
Click here to download

Video Lectures

🎥 Playlist: Introduction to Statistical Thoery Part - I
by Sher Muhammad Chuhdary
Ch:07 Random Variables
Watch on YouTube
🎥 Playlist: Introduction to Statistics by Naeem Bashir
Ch:07 Random Variables
Watch on YouTube

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