18.600 | Fall 2019 | Undergraduate

# Probability and Random Variables

## Calendar

SES # TOPICS KEY DATES
1 Permutations and combinations
2 Multinomial coefficients and more counting
3 Sample spaces and set theory
4 Axioms of probability
5 Probability and equal likelihood Problem Set 1 due
6 Conditional probabilities
7 Bayes’ formula and independent events
8 Discrete random variables Problem Set 2 due
9 Expectations of discrete random variables
10 Variance Problem Set 3 due
11 Binomial random variables, repeated trials and the so-called modern portfolio theory
12 Poisson random variables
13 Poisson processes Problem Set 4 due
14 More discrete random variables
15 Review for midterm exam 1
16 Midterm exam 1
17 Continuous random variables
18 Normal random variables Problem Set 5 due
19 Exponential random variables
20 More continuous random variables
21 Joint distribution functions Problem Set 6 due
22 Sums of independent random variables
23 Expectation of sums
24 Covariance and some conditional expectation exercises Problem Set 7 due
25 Conditional expectation
26 Moment generating functions
27 Weak law of large numbers Problem Set 8 due
28 Review for midterm exam 2
29 Midterm exam 2
30 Central limit theorem
31 Strong law of large numbers and Jensen’s inequality
32 Markov chains Problem Set 9 due
33 Entropy
34 Martingales and the optional stopping time theorem
35 Martingales and risk neutral probability
36 Risk neutral probability and Black-Scholes
37 Review for final exam Problem Set 10 due
38 Review for final exam (cont.)
39 Review for final exam (cont.)
40 Final exam

## Course Info

Fall 2019
##### Learning Resource Types
Problem Sets
Exams with Solutions
Lecture Notes
Online Textbook
Instructor Insights