--- title: Probability Distributions description: This area of mathematics describes the likelihood of different outcomes in a random event. Learners will understand discrete and continuous distributions, including normal, binomial, and Poisson distributions, and how to apply them to model real-world scenarios. category: programming-tech subcategory: data-science difficulty: beginner, intermediate, advanced url: /subject/probability-distributions --- # Probability Distributions This area of mathematics describes the likelihood of different outcomes in a random event. Learners will understand discrete and continuous distributions, including normal, binomial, and Poisson distributions, and how to apply them to model real-world scenarios. ## Available Resources 1 Videos • 2 Books • 4 Courses • 7 Websites ## Websites ### 1. Khan Academy Probability Video lessons and practice exercises on random variables, expected value, binomial and geometric distributions, and the normal distribution. After working through it you can compute probabilities and expectations for standard discrete and continuous distributions. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library **Tags:** probability, random-variables, probability-distributions, statistics ### 2. Seeing Theory An interactive, D3.js-based walkthrough of probability and statistics in six chapters, from basic probability and distributions through frequentist inference, Bayesian inference and regression analysis. Parameters are manipulable, so sampling behaviour and fit are visible directly. **Difficulty:** Beginner | **Price:** Free **Link:** https://seeing-theory.brown.edu/basic-probability/index.html **Tags:** probability, statistics, data-visualization, regression, bayesian-inference ### 3. StatLect Reference lectures covering the major discrete and continuous distributions, each with derivations of its density, moments, and defining properties. Readers finish able to recognise which distribution fits a problem and how the families relate to one another. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.statlect.com/probability-distributions **Tags:** probability-distributions, probability-theory, statistics, reference ### 4. Distributome An interactive navigator, searchable database, and calculators mapping named probability distributions and the relationships between them. Use it to look up a distribution's properties and to see how families connect through limits and transformations. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.distributome.org/ **Tags:** probability-distributions, interactive, reference, statistics ### 5. probabilitycourse.com ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://probabilitycourse.com **Tags:** websites, technology-computer-science, data-science--ai ### 6. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 7. seeing-theory.brown.edu Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://seeing-theory.brown.edu **Tags:** websites, technology-computer-science, data-science--ai ## Videos ### 1. Binomial distributions | Probabilities of probabilities, part 1 Animated walkthrough of the binomial distribution, using a product-review example to show how observed successes and failures translate into a probability density over an unknown underlying success rate. Explains where the binomial coefficient comes from. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=8idr1WZ1A7Q **Tags:** probability, binomial-distribution, bayesian-inference, visual-math ## Courses ### 1. Statistics 110: Probability Learn probability fundamentals with Harvard's Statistics 110 course, taught by Joe Blitzstein. Perfect for building a strong statistical foundation! **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo **Tags:** probability, conditional-probability, random-variables, markov-chains ### 2. Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC) **Author:** John Tsitsiklis Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/ **Tags:** probability, random-variables, bayesian-inference, limit-theorems, random-processes, statistical-inference ### 3. Fat Chance: Probability from the Ground Up **Author:** Benedict Gross, Joseph Harris, Emily Riehl A HarvardX introductory course that builds probability from counting principles: permutations, combinations, the binomial distribution, expected value, conditional probability, and the normal approximation. Learners develop the quantitative reasoning to calculate probabilities and assess risk in everyday and applied settings. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/probability/harvard-university-fat-chance-probability-from-the-ground-up **Tags:** probability, combinatorics, expected-value, binomial-distribution ### 4. An Intuitive Introduction to Probability **Author:** Karl Schmedders University of Zurich course taught by Karl Schmedders that builds probability from everyday examples: basic rules, conditional probability, applications, discrete random variables, and the normal distribution. Learners finish able to compute and interpret probabilities in practical decisions. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/introductiontoprobability **Tags:** probability, conditional-probability, discrete-random-variables, normal-distribution ## Books ### 1. Normal Normal - A book resource **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/095187070X?tag=edmonddante07-20 **Tags:** books, technology-computer-science, statistics-data-science ### 2. Probability and Statistics **Author:** Morris H. DeGroot, Mark J. Schervish A standard university textbook developing probability from its axioms through random variables, special distributions, and expectation, then building classical and Bayesian inference on that base. Covers estimation, sampling distributions, hypothesis testing, and linear models. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/711513913X?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, probability-theory --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/probability-distributions