Schedule

Introduction

9/22
Lecture
  • Introduction to class
  • Sample spaces and the naive definition of probability

Probability and counting

9/24
Lecture
  • How to count
9/25
HW 1 out due 10/2, 7 late days

Conditional probability

9/29
Lecture
  • Non-naive definition of probability
  • Definition of conditional probability
10/1
Lecture
  • Bayes’ rule and the law of total probability
10/2
HW 1 due due at 12pm, 7 late days
HW 2 out due 10/9, 7 late days
10/6
Lecture
  • Independence
  • Bayes’ rule continued

Random variables and their distributions

10/8
Lecture
  • Probability pitfalls and paradoxes
  • Random variables
  • Distributions and probability mass functions
10/9
HW 2 due due at 12pm, 7 late days
HW 3 out due 10/16, no late days
10/13
Lecture
  • Bernoulli and Binomial
  • Hypergeometric
10/15
Lecture
  • Discrete Uniform
  • Cumulative distribution functions
  • Functions of random variables
  • Independence of random variables
  • Definition of expectation
10/16
HW 3 due due at 12pm, no late days

Midterm

10/20
Midterm (in class)

Expectation

10/22
Lecture
  • Linearity of expectation
  • Geometric and Negative Binomial
10/23
HW 4 out due 10/30, 7 late days
10/27
Lecture
  • Indicator random variables
  • Law of the unconscious statistician
  • Variance

Continuous random variables

10/29
Lecture
  • Poisson
  • Probability density functions
10/30
HW 4 due due at 12pm, 7 late days
HW 5 out due 11/6, 7 late days
11/3
Lecture
  • Uniform
  • Normal
11/5
Lecture
  • Exponential
  • Poisson processes
  • Joint, marginal, and conditional
11/6
HW 5 due due at 12pm, 7 late days
HW 6 out due 11/13, 7 late days

Joint distributions

11/10
Lecture
  • Joint, marginal, and conditional
  • 2D Law of the Unconscious Statistician
11/12
Lecture
  • Covariance and correlation
  • Multinomial
  • Multivariate normal
11/13
HW 6 due due at 12pm, 7 late days
HW 7 out due 11/20, 7 late days

Transformations

11/17
Lecture
  • Change of variables
  • Convolutions
  • Gamma distribution

Conditional expectation

11/19
Lecture
  • Conditional expectation given an event
  • Conditional expectation given a random variable
11/20
HW 7 due due at 12pm, 7 late days
HW 8 out due 12/4, no late days
12/1
Lecture
  • Properties of conditional expectation
  • Conditional variance

Inequalities and limit theorems

12/3
Lecture
  • Inequalities
  • Law of large numbers
  • Central limit theorem
12/4
HW 8 due due at 12pm, no late days

Final exam

12/10
Final exam, 3:30-6:30pm