Lectures related to Probability Distributions: Moments and Transformations

Probability Distributions: Basics and Properties

Covers the basics of probability distributions, including mean, variance, and properties of random variables.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Vectors of Random Variables: Empirical Distributions

Discusses vectors of random variables and empirical distributions, including their properties and significance in statistics.

Statistics: Random Variables and Probability Density Functions

Introduces random variables, probability density functions, and Gaussian distribution in statistics.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Probability Distributions: Central Limit Theorem and Applications

Discusses probability distributions and the Central Limit Theorem, emphasizing their importance in data science and statistical analysis.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Variance of Random Variables

Covers the concept of variance for random variables and introduces calculation rules.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Air Pollution Analysis

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Probability Theory: Basics and Applications

Covers the fundamental concepts of probability theory and random variables.

Statistics: Exploratory Data Analysis

Introduces statistics basics, including data analysis and probability theory, emphasizing central tendency, dispersion, and distribution shapes.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.