In probability and statistics, many important quantities are found by accumulating small contributions over an interval. This idea appears when calculating areas under probability density curves, finding probabilities for continuous random variables, and computing expected values. In this module, you will develop the integration skills needed to understand these ideas. You will begin by interpreting area under a graph and accumulated change geometrically. From there, you will develop the definite integral through Riemann sums, explore important properties of integrals, and connect definite integrals with antiderivatives. Throughout the module, the emphasis is on understanding what an integral represents rather than simply carrying out symbolic calculations. These tools will provide the mathematical foundation for continuous probability distributions and other statistical models used throughout Statistics for Civic Life III.

In this module, you will study the probability distributions that form the foundation of statistical modeling. You will work with common discrete and continuous distributions, including the Uniform, Normal, and Exponential distributions, and use probability density functions, cumulative distribution functions, and integration to calculate probabilities. You will also use calculus to compute expected values, variances, and standard deviations. Finally, you will explore sampling distributions, the Law of Large Numbers, and the Central Limit Theorem to see how probability supports statistical inference.

In this final module, you will bring together the statistical and probability concepts developed throughout the course. You will review and synthesize key ideas, methods, and relationships across the modules, strengthening your ability to recognize when and how different concepts can be applied to solve statistical problems. You will then complete the comprehensive Final Exam, which provides an opportunity to demonstrate your overall mastery of the course material. Use this final assessment to apply what you have learned, interpret statistical and probabilistic results, and demonstrate your readiness to move forward with a deeper understanding of statistics.