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Created by:

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Last updated:

December 23, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


This course provides an elementary introduction to probability and statistics with applications.

Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.

The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.

Course Curriculum

    • Introduction, counting and sets Unlimited
    • Probability basics Unlimited
    • Conditional probability, Bayes’ theorem Unlimited
    • Discrete random variables, expectation Unlimited
    • Variance, continuous random variables Unlimited
    • Gallery of continuous variables, histograms Unlimited
    • Expectation, variance, law of large numbers and central limit theorem Unlimited
    • Joint distributions: Independence, covariance and correlation Unlimited
    • Review for exam 1 Unlimited
    • Introduction to statistics; maximum likelihood estimates Unlimited
    • Bayesian updating with known discrete priors Unlimited
    • Bayesian updating: Probabilistic prediction; odds Unlimited
    • Bayesian updating: Continuous prior, discrete data Unlimited
    • Beta distributions: Continuous data Unlimited
    • Conjugate priors; choosing priors Unlimited
    • Probability intervals Unlimited
    • Frequentist methods; NHST Unlimited
    • NHST II: Significance level, power, t-tests Unlimited
    • NHST III: Gallery of tests Unlimited
    • Comparison of Bayesian and frequentist inference Unlimited
    • Review for exam 2 Unlimited
    • Confidence intervals for normal data Unlimited
    • Confidence intervals II Unlimited
    • Bootstrap confidence intervals Unlimited
    • Linear regression Unlimited
    • Problems file: Review for final exam Unlimited
    • Solutions file: Review of final exam Unlimited
    • Problems file: Review for final exam, cont’d Unlimited
    • Solutions file: Review of final exam, cont’d Unlimited

About the instructor


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Massachusetts Institute of Technology
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