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This course introduces students to probability and random variables.
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1
English
English [CC]
FREE
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Description
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 content
- 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
Instructor
Massachusetts Institute of Technology
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1916
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