Lectures related to Signals & Systems I: Uncertainty Relations and Gabor Functions

Signals & Systems I: Uncertainty Relations and Gaussian Impulse

Explores uncertainty relations, Gaussian impulse, pseudo-probability density, and Gabor functions in signals and systems.

Continuous Random Variables

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

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Basics of Risk Analysis and Management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.

Introduction to Continuous Random Variables: Probability Distributions

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

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 Distributions: Testing and Estimation

Explores testing and estimating continuous distributions through interval partitioning and expected number calculations.

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Continuous Random Variables

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

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Normal Distribution: Characteristics and Examples

Covers the characteristics and importance of the normal distribution, including examples and treatment scenarios.

Nonuniform Random Number Distributions: Examples and Methods

Explores nonuniform random number distributions, examples, methods, and generation techniques.

Continuous Random Variables: Distributions and Expectation

Explores various continuous probability distributions and expectation of random variables.

Mixture models: alternative specific variance

Explores alternative specific variance in mixture models and discusses identification issues and model comparisons using 500 draws.

Air Pollution Analysis

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

Probability Distributions in Environmental Studies

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

Probability and Statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Elements of Statistics

Introduces key statistical concepts like probability, random variables, and correlation, with examples and explanations.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.