Probability and Statistics Course

Lesson 1 • Types of Data and Variables

Distinguishes categorical, ordinal, and continuous variables and their measurement scales. Establishes the vocabulary needed for all subsequent statistical analysis.

Lesson 2 • Descriptive Statistics: Central Tendency

Computes mean, median, and mode and interprets each in context. Provides the baseline summary tools used throughout the course.

Lesson 3 • Descriptive Statistics: Spread and Shape

Quantifies variability using range, variance, standard deviation, and IQR. Introduces skewness and kurtosis to characterize distribution shape.

Lesson 4 • Data Visualization for Decision Makers

Selects appropriate charts for variable types and audience needs. Reinforces descriptive concepts through visual interpretation.

Lesson 1 • Set Theory and Event Operations

Uses union, intersection, and complement to combine events. Provides the set-theoretic language for computing compound probabilities.

Lesson 2 • Bayes' Theorem and Updating Beliefs

Applies Bayes' theorem to revise probabilities given new evidence. Connects to real-world diagnostic and risk-assessment scenarios.

Lesson 3 • Probability Definitions and Axioms

Introduces classical, empirical, and subjective probability and the three Kolmogorov axioms. Grounds all later probability calculations in a rigorous framework.

Lesson 4 • Conditional Probability and Independence

Defines conditional probability and tests statistical independence between events. Directly supports Bayesian reasoning introduced in the next section.

Lesson 1 • Comparing and Selecting Discrete Models

Provides criteria for matching real data patterns to the appropriate discrete distribution. Reinforces model selection as a critical decision-making skill.

Lesson 2 • Poisson Distribution

Models rare event counts per unit of time or space using the Poisson parameter lambda. Connects to queuing, defect counting, and arrival-rate problems.

Lesson 3 • Geometric and Negative Binomial Distributions

Extends binary-trial models to waiting-time and repeated-success scenarios. Broadens the toolkit for modeling time-to-event data.

Lesson 4 • Binomial Distribution

Models fixed-trial binary outcomes using the binomial formula and parameters n and p. Applied to quality control, survey responses, and pass/fail scenarios.

Lesson 1 • The Normal Distribution

Parameterizes the normal curve by mean and standard deviation and uses z-scores for probability lookup. Central to inference chapters that follow.

Lesson 2 • Assessing Normality in Practice

Uses Q-Q plots, histograms, and formal tests to evaluate whether data fit a normal model. Prepares students to validate assumptions before applying parametric methods.

Lesson 3 • Exponential and Uniform Distributions

Models time-between-events with the exponential distribution and equal-likelihood outcomes with the uniform. Expands the continuous toolkit for operations and simulation.

Lesson 4 • Central Limit Theorem

Proves that sample means approach normality regardless of population shape as sample size grows. Justifies normal-based inference methods used in later chapters.

Lesson 1 • Point Estimation Principles

Defines estimators, bias, efficiency, and consistency as criteria for evaluating point estimates. Establishes the theoretical basis for choosing among competing estimators.

Lesson 2 • Confidence Intervals for Means

Constructs z-based and t-based confidence intervals for population means. Covers known and unknown variance scenarios with appropriate critical values.

Lesson 3 • Confidence Intervals for Proportions

Builds intervals for population proportions using the normal approximation. Directly applicable to survey analysis and quality-rate estimation.

Lesson 4 • Confidence Intervals for Variance

Uses the chi-square distribution to construct intervals for population variance and standard deviation. Extends estimation to variability parameters critical in quality management.

Lesson 1 • Tests for Variance: F and Chi-Square

Uses the F-test to compare two variances and chi-square tests for goodness of fit and independence. Extends hypothesis testing beyond mean-based comparisons.

Lesson 2 • One-Sample Tests for Means and Proportions

Applies z-tests and t-tests to single-sample mean problems and z-tests to proportions. Builds procedural fluency with the five-step testing framework.

Lesson 3 • Logic and Structure of Hypothesis Tests

Defines null and alternative hypotheses, Type I and Type II errors, and the p-value framework. Establishes the decision logic applied in every subsequent test.

Lesson 4 • Statistical Power and Error Control

Calculates power, beta error, and required sample sizes to achieve adequate test sensitivity. Connects error control to resource allocation in study design.

Lesson 1 • Simple Linear Regression

Estimates the least-squares line, interprets slope and intercept, and assesses model fit with R-squared. Provides the foundational regression workflow extended in later sections.

Lesson 2 • Inference in Simple Regression

Tests slope significance and constructs confidence and prediction intervals for regression outputs. Links regression to the hypothesis-testing framework from the previous chapter.

Lesson 3 • Multiple Linear Regression

Extends the model to multiple predictors, interprets partial slopes, and uses adjusted R-squared. Enables realistic multivariate decision modeling.

Lesson 4 • Correlation and Covariance

Measures linear association between two variables using Pearson correlation and covariance. Distinguishes correlation from causation before regression modeling begins.

Lesson 1 • Decision Trees and Sequential Choices

Builds and folds back decision trees incorporating probabilities and payoffs across multiple stages. Handles sequential decisions where earlier choices constrain later options.

Lesson 2 • Decision Theory Fundamentals

Introduces expected monetary value, utility theory, and decision criteria under risk and uncertainty. Frames statistical outputs as inputs to formal decision models.

Lesson 3 • Risk Metrics and Reporting

Summarizes simulation and analytical results using Value at Risk, confidence bounds, and risk dashboards. Translates statistical outputs into actionable executive communication.

Lesson 4 • Bayesian Decision Analysis

Updates prior beliefs with sample information to revise expected values and optimal choices. Demonstrates the full Bayesian cycle from prior to posterior decision.