18.440
Probability and Random Variables
Spring 2014
Topics
- Permutations and combinations
- Multinomial coefficients and more counting
- Sample spaces and set theory
- Axioms of probability
- Probability and equal likelihood
- Conditional probabilities
- Bayes’ formula and independent events
- Discrete random variables
- Expectations of discrete random variables
- Variance
- Binomial random variables, repeated trials and the so-called Modern Portfolio Theory
- Poisson random variables
- Poisson processes
- More discrete random variables
- Continuous random variables
- Uniform random variables
- Normal random variables
- Exponential random variables
- More continuous random variables
- Joint distribution functions
- Sums of independent random variables
- Expectation of sums
- Covariance and correlation
- Conditional expectation
- Moment generating distributions
- Weak law of large numbers
- Central limit theorem
- Strong law of large numbers and Jensen’s inequality
- Markov chains
- Entropy
- Martingales and the Optional Stopping Time Theorem
- Risk Neutral Probability and Black-Scholes
Readings
- Readings are assigned from the required textbook.
- Ross, Sheldon. A First Course in Probability . 8th ed. Pearson Prentice Hall, 2009. ISBN: 9780136033134.
- SES #: 3 · TOPICS: Sample spaces and set theory · READINGS: Sections 2.1–2.2
- SES #: 4 · TOPICS: Axioms of probability · READINGS: Sections 2.3–2.4
- SES #: 7 · TOPICS: Bayes’ formula and independent events · READINGS: Sections 3.3–3.5
- SES #: 8 · TOPICS: Discrete random variables · READINGS: Sections 4.1–4.2
- SES #: 10 · TOPICS: Variance · READINGS: Section 4.5
- SES #: 12 · TOPICS: Poisson random variables · READINGS: Section 4.7
- SES #: 13 · TOPICS: Poisson processes · READINGS: Section 9.1
- SES #: 14 · TOPICS: More discrete random variables · READINGS: Sections 4.8–4.9
- SES #: 15 · TOPICS: Continuous random variables · READINGS: Sections 5.1–5.2
- SES #: 18 · TOPICS: Uniform random variables · READINGS: Section 5.3
- SES #: 19 · TOPICS: Normal random variables · READINGS: Section 5.4
- SES #: 20 · TOPICS: Exponential random variables · READINGS: Section 5.5
- SES #: 21 · TOPICS: More continuous random variables · READINGS: Sections 5.6–5.7
- SES #: 22 · TOPICS: Joint distribution functions · READINGS: Sections 6.1–6.2
- SES #: 23 · TOPICS: Sums of independent random variables · READINGS: Sections 6.3–6.5
- SES #: 24 · TOPICS: Expectation of sums · READINGS: Sections 7.1-7.2
- SES #: 25 · TOPICS: Covariance · READINGS: Sections 7.3–7.4
- SES #: 26 · TOPICS: Conditional expectation · READINGS: Sections 7.5–7.6
- SES #: 27 · TOPICS: Moment generating distributions · READINGS: Sections 7.7–7.8
- SES #: 30 · TOPICS: Weak law of large numbers · READINGS: Sections 8.1–8.2
- SES #: 31 · TOPICS: Central limit theorem · READINGS: Section 8.3
- SES #: 33 · TOPICS: Markov chains · READINGS: Section 9.2
- SES #: 34 · TOPICS: Entropy · READINGS: Sections 9.3–9.4
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.