Schedule

Introduction

9/23

Lecture

• Introduction to class

• Sample spaces and the naive definition of probability

• Textbook reading: 1.1-1.3

• Course reader: 1.1-1.3

• Introductory slides (PDF)

Probability and counting

9/25

Lecture

• How to count

• Textbook reading: 1.4-1.5

• Course reader: 1.4

9/26

HW 1 out due 10/3, 7 late days

Conditional probability

9/30

Lecture

• Non-naive definition of probability

• Definition of conditional probability

• Textbook reading: 1.6, 2.1-2.2

• Course reader: 1.5, 2.1

10/2

Lecture

• Bayes’ rule and the law of total probability

• Textbook reading: 2.3-2.4

• Course reader: 2.2

10/3

HW 1 due due at 12pm, 7 late days

HW 2 out due 10/10, 7 late days

10/7

Lecture

• Independence

• Bayes’ rule continued

• Textbook reading: 2.5-2.7

• Course reader: 2.3-2.4

Random variables and their distributions

10/9

Lecture

• Probability pitfalls and paradoxes

• Random variables

• Distributions and probability mass functions

• Textbook reading: 2.8, 3.1-3.2

• Course reader: 2.5, 3.1-3.2

10/10

HW 2 due due at 12pm, 7 late days

HW 3 out due 10/17, 7 late days

10/14

Lecture

• Bernoulli and Binomial

• Hypergeometric

• Textbook reading: 3.3-3.4

• Course reader: 3.3-3.4

10/16

Lecture

• Discrete Uniform

• Cumulative distribution functions

• Functions of random variables

• Independence of random variables

• Definition of expectation

• Textbook reading: 3.5-3.8, 4.1

• Course reader: 3.5-3.8, 4.1

10/17

HW 3 due due at 12pm, 7 late days

HW 4 out due 10/24, no late days

Expectation

10/21

Lecture

• Linearity of expectation

• Geometric and Negative Binomial

• Textbook reading: 4.2-4.3

• Course reader: 4.2-4.3

10/23

Lecture

• Indicator random variables

• Law of the unconscious statistician

• Variance

• Textbook reading: 4.4-4.6

• Course reader: 4.4-4.6

10/24

HW 4 due due at 12pm, no late days

Midterm

10/28

Midterm (in class)

Continuous random variables

10/30

Lecture

• Poisson

• Probability density functions

• Textbook reading: 4.7, 5.1

• Course reader: 4.7, 5.1

10/31

HW 5 out due 11/7, 7 late days

11/4

Lecture

• Uniform

• Normal

• Textbook reading: 5.2, 5.4

• Course reader: 5.2-5.3

11/6

Lecture

• Exponential

• Poisson processes

• Joint, marginal, and conditional

• Textbook reading:5.5-5.6. 7.1

• Course reader: 5.4-5.5, 6.1

11/7

HW 5 due due at 12pm, 7 late days

HW 6 out due 11/14, 7 late days

Joint distributions

11/11

Lecture

• Joint, marginal, and conditional

• 2D Law of the Unconscious Statistician

• Textbook reading: 7.1-7.2

• Course reader: 6.1-6.2

11/13

Lecture

• Covariance and correlation

• Multinomial

• Multivariate normal

• Textbook reading: 7.3-7.5

• Course reader: 6.3-6.5

• Bivariate normal slides (PPT)

11/14

HW 6 due due at 12pm, 7 late days

HW 7 out due 11/21, 7 late days

Transformations

11/18

Lecture

• Change of variables

• Convolutions

• Gamma distribution

• Textbook reading: 8.1-8.2, 8.4

• Course reader: 7.1-7.3

Conditional expectation

11/20

Lecture

• Conditional expectation given an event

• Conditional expectation given a random variable

• Textbook reading: 9.1-9.2

• Course reader: 8.1-8.2

11/21

HW 7 due due at 12pm, 7 late days

HW 8 out due 12/5, no late days

12/2

Lecture

• Properties of conditional expectation

• Conditional variance

• Textbook reading: 9.3, 9.5-9.6

Inequalities and limit theorems

12/4

Lecture

• Inequalities

• Law of large numbers

• Central limit theorem

• Textbook reading: 10.1-10.3

12/5

HW 8 due due at 12pm, no late days

Final exam

12/11

Final exam, 3:30-6:30pm