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Johns Hopkins University

Statistics for Civic Life III: Probability & Chance

Johns Hopkins University via Coursera

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Overview

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In this course, you will build a foundation in probability and random variables and learn how these ideas are used to model uncertainty. You will work with both discrete and continuous random variables, calculate probabilities, expected values, and variances, and study important probability distributions. Topics include conditional probability, discrete distributions, and continuous distributions such as the Uniform, Normal, and Exponential distributions. The course also introduces the basic calculus needed to work with continuous probability models, including integration for computing probabilities and expected values. Throughout the course, you will apply probability concepts to practical problems involving risk, uncertainty, data, and real-world decision-making. By the end of the course, you will be able to construct and interpret probability models, analyze discrete and continuous random variables, and use mathematical tools to better understand uncertain outcomes.

Syllabus

  • Module 1: Introduction to Probability
    • In this module, you will build a foundation in probability and learn how it is used to describe uncertainty and randomness. You will apply probability rules, conditional probability, independence, and counting techniques such as tree diagrams, permutations, and combinations. You will also study discrete and continuous probability models, expected value, and distributions such as the Binomial and Normal. Using RStudio, you will simulate random experiments, compare theoretical probabilities with empirical results, and apply probability methods to practical problems.
  • Finding Area using Integration
    • 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.
  • Module 3: Continuous and Discrete Distributions
    • 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.
  • Final Exam
    • 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.

Taught by

Joseph W. Cutrone, PhD and Justine Stauffer

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