Lectures related to Indicator function

Central Limit Theorem

Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.

Random variables and their expectations

Covers random variables in a finite probability space, expectations, and event indicators.

Characteristic Functions: Properties and Applications

Covers characteristic functions, their properties, inversion formula, and factorization property in probability theory.

Polymer Behavior: Force-Extension Curve

Delves into the entropic behavior of polymers through force-extension curves.

Central Limit Theorem: Characteristic Functions

Explores an alternative proof of the Central Limit Theorem using characteristic functions to show the emergence of the Gaussian distribution.

Statistical Thermodynamics: Density of States

Explores density of states in statistical thermodynamics and the use of Heaviside functions for energy level probabilities.

Linearity of Expectation: First Moment Method

Introduces Linearity of Expectation and the First Moment Method, explores probability theory problems like Buffon's Needle, and discusses transitive tournaments and Ham paths.

Implicit Functions: Local Existence Theorem

Discusses implicit functions and the local existence theorem for finding solutions.

Signals & Systems II: Statistical Properties and Optimal Detectors

Explores conditional probabilities, characteristic functions, and optimal detectors in signals and systems.

Conditional Probabilities and Independence

Explores conditional probabilities, independence, characteristic functions, and optimal detectors for signal detection.

Probabilités discrètes

Covers the basics of discrete probability, including notations, axioms, pmf, examples, expectation, variance, and indicator variables.

Stochastic Models for Communications: Markov Chains and Random Variables

Covers Markov chains, random variables, independence, characteristic functions, and queueing theory.

Random Vectors: Stochastic Models for Communications

Covers random vectors, joint probability, and Gaussian random variables in communication models.

Multivariate Statistics: Introduction and Methods

Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.

Kolmogorov's Three Series Theorem

Explores Kolmogorov's 0-1 law, convergence of random variables, tightness, and characteristic functions.

Probability and Measure: Fundamentals and Applications

Covers fundamental concepts of probability theory and measure theory, including joint probabilities, random variables, and the central limit theorem.

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Complement: Convergence in Distribution

Explores convergence in distribution of random variables and characteristic functions.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Generating Functions: Moments and Cumulants

Explores generating functions for moments and cumulants, showcasing their role in distribution analysis.