Lectures in course MATH-234(a): Probability and statistics

Covers the fundamentals of statistics, exploring probabilistic models, variability, uncertainty, and data collection.

Explains quantiles, functions of random variables, conditional densities, and variable transformations.

Explores statistical inference for linear models, covering model fitting, parameter estimation, and variance decomposition.

Covers the basics of exploratory statistics, including variables, quantiles, central tendency, dispersion, outliers, and robustness.

Explores break points in statistics and the nuances of correlation analysis.

Explores data distribution strategies, normal modeling, and checking normality with graphical tools.

Explores continuous random variables, density functions, and distribution laws with practical examples.

Explains joint random variables, marginal laws, and independence implications.

Covers the basics of probability theory, including events, intersections, unions, and probabilities.

Covers the concepts of expectation and variance in statistics, including their calculations and significance.

Explains probability laws, event spaces, and confidence levels in event occurrences.

Explores conditional and total probabilities, including the practical application of Bayes theorem.

Explores variance, covariance, and correlation in statistics, essential for data analysis.

Explores probability, independence, and system reliability in decision-making processes and event occurrences.

Explores fundamental theorems in statistics, including laws of large numbers and the central limit theorem.

Explores constructing a probability model, random sampling, variance calculation, and allocation optimization in experiments.

Explores discrete random variables, their functions, and probabilities in various scenarios.

Explores statistical models, sampling distributions, and hypothesis testing using real-world examples.

Explores binomial and Poisson mass functions, calculating probabilities and discussing distribution functions of random variables.

Explains hypothesis testing using T-test and Chi-square test to compare means and assess independence of variables.