This website is an interactive educational application developed to simulate and visualize various statistical concepts:

Law of Large Numbers
Central Limit Theorem
Confidence Intervals
Hypothesis Testing
ANOVA
Joint Distributions
Least Squares
Sample Distribution of OLS Estimators
The OLS Estimators are Consistent
Omitted Variable Bias
Multiple Regression

Project of Professor Tanya Byker and Professor Amanda Gregg at Middlebury College, with research assistants Kevin Serrao, Class of 2018, Dylan Mortimer, Class of 2019, Ammar Almahdy, Class of 2020, Jacqueline Palacios, Class of 2020, Siyuan Niu, Class of 2021, David Gikoshvili, Class of 2021, and Ethan Saxenian, Class of 2022.

Offered during MIT’s Independent Activites Period (IAP), this short course covers the poker concepts, math concepts, and general concepts needed to play the game of Texas Hold’em on a professional level.
IAP is a special 4-week term in January that provides members of the MIT community including students, faculty, staff, and alums with an opportunity to organize, sponsor and participate in a wide variety of activities and topics that are often outside of the regular MIT curriculum.
Faculty Advisor: Paul Mende

6.0002 is the continuation of 6.0001 Introduction to Computer Science and Programming in Python and is intended for students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems and to help students, regardless of their major, feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class uses the Python 3.5 programming language.

This course will provide a solid foundation in probability and statistics for economists and other social scientists. We will emphasize topics needed for further study of econometrics and provide basic preparation for 14.32 Econometrics. Topics include elements of probability theory, sampling theory, statistical estimation, and hypothesis testing.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Samples and ProbabilityType of Unit: ConceptualPrior KnowledgeStudents should be able to:Understand the concept of a ratio.Write ratios as percents.Describe data using measures of center.Display and interpret data in dot plots, histograms, and box plots.Lesson FlowStudents begin to think about probability by considering the relative likelihood of familiar events on the continuum between impossible and certain. Students begin to formalize this understanding of probability. They are introduced to the concept of probability as a measure of likelihood, and how to calculate probability of equally likely events using a ratio. The terms (impossible, certain, etc.) are given numerical values. Next, students compare expected results to actual results by calculating the probability of an event and conducting an experiment. Students explore the probability of outcomes that are not equally likely. They collect data to estimate the experimental probabilities. They use ratio and proportion to predict results for a large number of trials. Students learn about compound events. They use tree diagrams, tables, and systematic lists as tools to find the sample space. They determine the theoretical probability of first independent, and then dependent events. In Lesson 10 students identify a question to investigate for a unit project and submit a proposal. They then complete a Self Check. In Lesson 11, students review the results of the Self Check, solve a related problem, and take a Quiz.Students are introduced to the concept of sampling as a method of determining characteristics of a population. They consider how a sample can be random or biased, and think about methods for randomly sampling a population to ensure that it is representative. In Lesson 13, students collect and analyze data for their unit project. Students begin to apply their knowledge of statistics learned in sixth grade. They determine the typical class score from a sample of the population, and reason about the representativeness of the sample. Then, students begin to develop intuition about appropriate sample size by conducting an experiment. They compare different sample sizes, and decide whether increasing the sample size improves the results. In Lesson 16 and Lesson 17, students compare two data sets using any tools they wish. Students will be reminded of Mean Average Deviation (MAD), which will be a useful tool in this situation. Students complete another Self Check, review the results of their Self Check, and solve additional problems. The unit ends with three days for students to work on Gallery problems, possibly using one of the days to complete their project or get help on their project if needed, two days for students to present their unit projects to the class, and one day for the End of Unit Assessment.

Students will compare expected results to actual results by first calculating the probability of an event, then conducting an experiment to generate data. They will use an interactive to simulate a familiar event—rolling a number cube. Students will also be introduced to terminology.Key ConceptsThis lesson takes an informal look at the Law of Large Numbers through comparing experimental results to expected results.There is variability in actual results.Probability terminology is introduced:theoretical probability: the ratio of favorable outcomes to the total number of possible equally-likely outcomes, often simply called probabilityexpected results: the results based on theoretical probabilityexperimental probability: the ratio of favorable outcomes to the total number of trials in an experimentactual results: the results based on experimental probabilityoutcome: a single possible resultsample space: the set of all possible outcomesexperiment: a controlled, repeated process, such as repeatedly tossing a cointrial: each repetition in an experiment, such as one coin tossevent: a set of outcomes to which a probability is assignedGoals and Learning ObjectivesPredict results using ratio and proportion.Compare expected results to actual results.Understand that the actual results get closer to the expected results as the number of trials increase.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

This 9-minute video lesson provides an introduction to the law of large numbers. [Statistics playlist: Lesson 27 of 85]

Provides students with the basic tools for analyzing experimental data, properly interpreting statistical reports in the literature, and reasoning under uncertain situations. Topics organized around three key theories: Probability, statistical, and the linear model. Probability theory covers axioms of probability, discrete and continuous probability models, law of large numbers, and the Central Limit Theorem. Statistical theory covers estimation, likelihood theory, Bayesian methods, bootstrap and other Monte Carlo methods, as well as hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory covers the simple regression model and the analysis of variance. Places equal emphasis on theory, data analyses, and simulation studies.