This course on Basic Limit Theorems aims to help learners understand various modes of convergence, including convergence in probability and almost sure convergence. The course covers important theorems such as Levy Continuity Theorem, Central Limit Theorem, Law of Large Numbers, and Continuous Mapping Theorem. By the end of the course, students will be equipped with the skills to apply Slutsky's Theorem and understand the implications of different limit theorems. The teaching method involves theoretical explanations, examples, and proofs. This course is intended for individuals interested in statistics, probability theory, or related fields who want to deepen their understanding of limit theorems.
Overview
Syllabus
Basic Limit Theorems (1/11): Some Modes of Convergence.
Basic Limit Theorems (2/11): Convergence in probability implies convergence in Distribution.
Basic Limit Theorems (3/11): Convergence Almost Surely Implies Convergence in Probabilty.
Basic Limit Theorems (4/11): Examples with Modes of Convergence.
Basic Limit Theorems (5/11): Levy Continuity Theorem. Polya Theorem..
Basic Limit Theorems (6/11): Central Limit Theorem.
Basic Limit Theorems (7/11): Law of Large Numbers.
Basic Limit Theorems (8/11): Proof of WLLN without Assumption of Finite Variane.
Basic Limit Theorems (9/11): Continuous Mapping Theorem.
Basic Limit Theorems (10/11): Slutsky's Theorem.
Chi square approximation to an F Distribution.
Nth Order Statistic from a Uniform Converges in Distribution to an Exponential.
Lindeberg CLT Condition not Satisfied. Variable Still Converges to a Standard Normal..
Some Inplications of the Lindeberg Central Limit Theorem.
Lyapunov's Central Limit Theorem.
Proof of Lindeberg's Central Limit Theorem.
Proof that (1+a/n)^(bn) converges to e^(ab).
Taught by
statisticsmatt
Related Courses
-
Probability: Distribution Models & Continuous Random Variables
-
Probability Theory: Foundation for Data Science
-
Introduction to Probability
5.0 -
Probability - The Science of Uncertainty and Data
4.9 -
Central Limit Theorem - Sampling Distribution of Sample Means - Stats & Probability
-
A Basic Course in Real Analysis
