Lectures in course MATH-236: Probability and statistics II

Combinatorics: Counting Methods

Introduces combinatorics and counting methods for determining possible outcomes in various scenarios, illustrated with examples.

Probability and Events

Covers sample space, events, probability interpretation, axioms, and useful theorems.

Goodness-of-fit Tests in Statistics

Explores goodness-of-fit tests, X² tests, and independence tests in statistics, with practical examples and applications.

Statistical Tests: Independence and Homogeneity

Explores statistical tests for independence and homogeneity, including chi-square tests and Fisher's exact test, with practical examples and applications.

Point Estimation Methods: MOM and MLE

Explores point estimation methods like MOM and MLE, discussing bias, variance, and examples.

Maximum Likelihood Estimation: Theory and Applications

Explores likelihood in probability, maximum likelihood estimation, and its applications in statistical inference.

Maximum Likelihood Estimation: Properties and Applications

Explores the properties and challenges of Maximum Likelihood Estimators.

Logistic Regression: Modeling Binary Response Variables

Explores logistic regression for binary response variables, covering topics such as odds ratio interpretation and model fitting.

Logistic Regression: Model Interpretation and Comparison

Explores logistic regression model interpretation, parameter estimation, and model comparison using likelihood ratio tests.

Probability and Statistics II: Estimation and Hypothesis Testing

Covers the Central Limit Theorem, confidence intervals, hypothesis testing, and qualities of estimators.

Estimation Methods: Bias-Variance Tradeoff

Explores the MSE quality measure for estimators and the bias-variance tradeoff.

Statistical Hypothesis Testing: Inference and Interpretation

Explores statistical hypothesis testing, including constructing confidence intervals, interpreting p-values, and making decisions based on significance levels.

Hypothesis Testing & Confidence Intervals

Covers hypothesis testing, power, confidence intervals, and small sample considerations.

Statistical Modeling: Estimation and Hypothesis Testing

Covers statistical modeling, estimation, CLT, confidence intervals, and hypothesis testing steps with practical examples.

Modeling Bivariate Data: Linear Regression

Explores bivariate data, linear regression modeling, and correlation in scientific investigations and research processes.

Linear Regression: Concepts and Applications

Introduces linear regression concepts, from X-bands creation to slope estimator properties and tests.

Regression Analysis: Multivariate Data Modeling

Introduces regression analysis for multivariate data modeling, covering matrix algebra, interpretation of coefficients, and test intervals.

Regression Analysis: Interpretation and Applications

Explores multiple regression, ANOVA, interpretation of coefficients, and regression estimation.

Analysis of Variance: Principles and Applications

Explores the principles and applications of Analysis of Variance (ANOVA), including test hypotheses, models, assumptions, and post-hoc tests.

ANOVA and Factorial Experiments

Explores ANOVA, factorial experiments, and model evaluation techniques.