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ECDF and Quantiles
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Law of Large Numbers: Probability
Explores the convergence of averages of random variables and empirical frequencies in probability theory.
Families of Distributions: PDFs and CDFs
Explores PDFs and CDFs for discrete and continuous random variables, including Gaussian, uniform, and exponential distributions.
Fracture Mechanics: Crack Growth and Weakest Link
Explores fracture mechanics, crack growth, and the weakest link theory, emphasizing the statistical distribution of crack sizes and the significance of the largest crack in material failure.
Calculating Growth Rates
Explores the calculation of growth rates, average GDP growth, and environmental footprint changes.
Average Growth Rates Calculation
Explains how to calculate average growth rates using arithmetic mean, geometric mean, and linear trend analysis.
Exploratory Statistics: Understanding Populations and Samples
Covers exploratory statistics, focusing on populations, samples, and various statistical measures.
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: Moments and Transformations
Covers moments computation and probability distribution transformations.
Normal Distribution: Properties and Calculations
Covers properties and calculations related to the normal distribution, including probabilities and quantiles.
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.