Lectures: MWF 11-12, 4.370

Office hours: Monday 1-2 and Wednesday 2-3, 2-180

TA: Zhenqi He

TA Office hours: Thursday 4-6, 2-102

Text: A First Course in Probability, 8th edition, by Sheldon Ross

Assignments: Homeworks (10%), midterm exams (40%), final exam (50%)

TENTATIVE SCHEDULE

- Lecture 1 (September 9): 1.1-1.3 Permutations and combinations (also Pascal's triangle --- as studied (not invented) by Pascal, see also correspondence with Fermat. )
- Lecture 2 (September 11): 1.4-1.5 Multinomial coefficients and more counting
- Lecture 3 (September 14): 2.1-2.2 Sample spaces and set theory
- Lecture 4 (September 16): 2.3-2.4 Axioms of probability
- Lecture 5 (September 18): 2.5-2.7 Probability and equal likelihood (and a bit more history and a famous hat problem)
- Lecture 6 (September 21): 3.1-3.2 Conditional probabilities
- Lecture 7 (September 23): 3.3-3.5 Bayes' formula and independent events
- Lecture 8 (September 25): 4.1-4.2 Discrete random variables
- Lecture 9 (September 28): 4.3-4.4 Expectations of discrete random variables (and, for non-discrete setting, examples of non-measurable sets, as in the Vitali construction)
- Lecture 10 (September 30): 4.5 Variance
- Lecture 11 (October 2): 4.6 Binomial random variables, repeated trials and the so-called Modern Portfolio Theory.
- Lecture 12 (October 5): 4.7 Poisson random variables
- Lecture 13 (October 7): 9.1 Poisson processes
- Lecture 14 (October 9): 4.8-4.9 More discrete random variables
Practice Midterm Exam (here is an old midterm and see also Jonathan Kelner's old 18.440 pages)

- Lecture 15 (October 13): REVIEW
- Lecture 16 (October 14): MIDTERM EXAM on CHAPTERS 1-4 (plus 9.1)
- Lecture 17 (October 16): 5.1-5.2 Continuous random variables
- Lecture 18 (October 19): 5.3 Uniform random variables
- Lecture 19 (October 21): 5.4 Normal random variables
- Lecture 20 (October 23): 5.5 Exponential random variables
- Lecture 21 (October 26): 5.6-5.7 More continuous random variables
- Lecture 22 (October 28): 6.1-6.2 Joint distribution functions
- Lecture 23 (October 30): 6.3-6.5 Sums of independent random variables
- Lecture 24 (November 2): 7.1-7.2 Expectation of sums
- Lecture 25 (November 4): 7.3-7.4 Covariance
- Lecture 26 (November 6): 7.5-7.6 Conditional expectation
- Lecture 27 (November 9): 7.7-7.8 Moment generating distributions
Practice Midterm Exam Two (and another source for old exam reviews)

- Lecture 28 (November 13): REVIEW
- Lecture 29 (November 16): MIDTERM EXAM on 1-7 (plus 9.1)
Midterm Two with solutions

- Lecture 30 (November 18): 8.1-8.2 Weak law of large numbers
- Lecture 31 (November 20): 8.3 Central limit theorem
- Lecture 32 (November 23): 8.4-8.5 Strong law of large numbers (see also the truncation-based proof on Terry Tao's blog and the characteristic function proof of the weak law) and Jensen's inequality.
- Lecture 33 (November 25): 9.2 Markov chains
- Lecture 34 (November 30): 9.3-9.4 Entropy
- Lecture 35 (December 2): Martingales and the Optional Stopping Time Theorem (see also prediction market plots)
- Lecture 36 (December 4): Risk Neutral Probability and Black-Scholes (look up options quotes at the Chicago Board Options Exchange)
- Lecture 37 (December 7): REVIEW
- Lecture 38 (December 9): REVIEW
- (Week of December 14-18): Final Exam