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Created by:

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Last updated:

December 26, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


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.

Course Curriculum

  • Permutations and Combinations Unlimited
  • Multinomial Coefficients and More Counting Unlimited
  • Sample Spaces and Set Theory Unlimited
  • Axioms of Probability Unlimited
  • Probability and Equal Likelihood Unlimited
  • Conditional Probabilities Unlimited
  • Bayes’ Formula and Independent Events Unlimited
  • Discrete Random Variables Unlimited
  • Expectations of Discrete Random Variables Unlimited
  • Variance Unlimited
  • Binomial Random Variables, Repeated Trials and the so-called Modern Portfolio Theory Unlimited
  • Poisson Random Variables Unlimited
  • Poisson Processes Unlimited
  • More Discrete Random Variables Unlimited
  • Continuous Random Variables Unlimited
  • Review for Midterm Exam 1 Unlimited
  • Uniform Random Variables Unlimited
  • Normal Random Variables Unlimited
  • Exponential Random Variables Unlimited
  • More Continuous Random Variables Unlimited
  • Joint Distribution Functions Unlimited
  • Sums of Independent Random Variables Unlimited
  • Expectation of Sums Unlimited
  • Covariance and Correlation Unlimited
  • Conditional Expectation Unlimited
  • Moment Generating Distributions Unlimited
  • Review for Midterm Exam 2 Unlimited
  • Weak Law of Large Numbers Unlimited
  • Central Limit Theorem Unlimited
  • Strong Law of Large Numbers and Jensen’s Inequality Unlimited
  • Markov Chains Unlimited
  • Entropy Unlimited
  • Martingales and the Optional Stopping Time Theorem Unlimited
  • Risk Neutral Probability and Black-Scholes Unlimited
  • Review for Final Exam Unlimited
  • Review for Final Exam (cont.) Unlimited
  • Review for Final Exam (cont.) Unlimited

About the instructor


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Massachusetts Institute of Technology
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