Lectures in course MATH-131: Probability and statistics

Covers fundamental concepts of probability and statistics, focusing on data analysis, graphical representation, and practical applications.

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

Explores PDF forms, statistics, boxplots, density curves, and data analysis methods.

Introduces statistical analysis concepts like boxplot and normal distribution using real data examples.

Introduces key concepts in probability and statistics, such as events, Venn diagrams, and conditional probability.

Explores Bayes' Theorem for defective parts detection, discrete random variables, and distribution functions, with practical examples and exercises.

Explores joint random variables, conditional density, and independence in probability and statistics.

Explores conditional density, expectations, and independence of random variables with practical examples.

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Explores statistical models, parameter estimation, and sampling distributions in probability and statistics.

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

Explores confidence intervals, hypothesis testing, and decision-making using test statistics and p-values.

Explains the Chi-Square test for independence hypothesis and its practical applications.

Covers the estimation of theoretical frequencies and independence testing between two characteristics, with examples for practical application.

Explores linear regression analysis of ozone data using statistical models.