18.600
Probability and Random Variables
Probability spaces, random variables, distribution functions. Binomial, geometric, hypergeometric, Poisson distributions. Uniform, exponential, normal, gamma and beta distributions. Conditional probability, Bayes theorem, joint distributions. Chebyshev inequality, law of large numbers, and central limit theorem. Credit cannot also be received for 6.041A or 6.041B.
Fall 2019
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
- Normal random variables
- Exponential random variables
- More continuous random variables
- Joint distribution functions
- Sums of independent random variables
- Expectation of sums
- Covariance and some conditional expectation exercises
- Conditional expectation
- Moment generating functions
- 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
- Martingales and risk neutral probability
- 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 #: 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 #: 13 · TOPICS: Poisson processes · READINGS: Section 9.1
- SES #: 14 · TOPICS: More discrete random variables · READINGS: Sections 4.8–4.9
- SES #: 17 · TOPICS: Continuous random variables · READINGS: Sections 5.1–5.3
- SES #: 18 · TOPICS: Normal random variables · READINGS: Section 5.4
- SES #: 19 · TOPICS: Exponential random variables · READINGS: Section 5.5
- SES #: 20 · TOPICS: More continuous random variables · READINGS: Sections 5.6–5.7
- SES #: 21 · TOPICS: Joint distribution functions · READINGS: Sections 6.1–6.2
- SES #: 22 · TOPICS: Sums of independent random variables · READINGS: Sections 6.3–6.5
- SES #: 23 · TOPICS: Expectation of sums · READINGS: Sections 7.1-7.2
- SES #: 24 · TOPICS: Covariance and some conditional expectation exercises · READINGS: Sections 7.3-7.4
- SES #: 25 · TOPICS: Conditional expectation · READINGS: Sections 7.5–7.6
- SES #: 26 · TOPICS: Moment generating functions · READINGS: Sections 7.7–7.8
- SES #: 27 · TOPICS: Weak law of large numbers · READINGS: Sections 8.1–8.2
- SES #: 30 · TOPICS: Central limit theorem · READINGS: Section 8.3
- SES #: 32 · TOPICS: Markov chains · READINGS: Section 9.2
- SES #: 33 · TOPICS: Entropy · READINGS: Sections 9.3–9.4
Prerequisites & course information
Prereq: Calculus II (GIR) U (Fall, Spring) 4-0-8 units. REST Credit cannot also be received for 6.3700 , 6.3702
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2019
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.