Schedule

Introduction

Wed, Sep. 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

Probability and counting

Fri, Sep. 25

Lecture

• How to count

• Textbook reading: 1.4-1.5

• Course reader: 1.4

Conditional probability

Wed, Sep. 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

Fri, Oct. 2

Lecture

• Bayes’ rule and the law of total probability

• Textbook reading: 2.3-2.4

• Course reader: 2.2

Mon, Oct. 5

Quiz 1

Wed, Oct. 7

Lecture

• Independence

• Bayes’ rule continued

• Textbook reading: 2.5-2.7

• Course reader: 2.3-2.4

Random variables and their distributions

Fri, Oct. 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

Mon, Oct. 12

Quiz 2

Wed, Oct. 14

Lecture

• Bernoulli and Binomial

• Hypergeometric

• Textbook reading: 3.3-3.4

• Course reader: 3.3-3.4

Fri, Oct. 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

Mon, Oct. 19

Quiz 3

Expectation

Wed, Oct. 21

Lecture

• Linearity of expectation

• Geometric and Negative Binomial

• Textbook reading: 4.2-4.3

• Course reader: 4.2-4.3

Fri, Oct. 23

Lecture

• Indicator random variables

• Law of the unconscious statistician

• Variance

• Textbook reading: 4.4-4.6

• Course reader: 4.4-4.6

Mon, Oct. 26

Quiz 4

Continuous random variables

Wed, Oct. 28

Lecture

• Poisson

• Probability density functions

• Textbook reading: 4.7, 5.1

• Course reader: 4.7, 5.1

Fri, Oct. 30

Lecture

• Uniform

• Normal

• Textbook reading: 5.2, 5.4

• Course reader: 5.2-5.3

Mon, Nov. 2

Quiz 5

Wed, Nov. 4

Lecture

• Exponential

• Poisson processes

• Joint, marginal, and conditional

• Textbook reading: 5.5-5.6, 7.1

• Course reader: 5.4-5.5, 6.1

Joint distributions

Fri, Nov. 6

Lecture

• Joint, marginal, and conditional

• 2D Law of the Unconscious Statistician

• Textbook reading: 7.1-7.2

• Course reader: 6.1-6.2

Mon, Nov. 9

Quiz 6

Wed, Nov. 11

Lecture

• Covariance and correlation

• Multinomial

• Multivariate normal

• Textbook reading: 7.3-7.5

• Course reader: 6.3-6.5

• Bivariate normal slides (PPT)

Transformations

Fri, Nov. 13

Lecture

• Change of variables

• Convolutions

• Gamma distribution

• Textbook reading: 8.1-8.2, 8.4

• Course reader: 7.1-7.3

Mon, Nov. 16

Quiz 7

Conditional expectation

Wed, Nov. 18

Lecture

• Conditional expectation given an event

• Conditional expectation given a random variable

• Textbook reading: 9.1-9.2

• Course reader: 8.1-8.2

Fri, Nov. 20

Lecture

• Properties of conditional expectation

• Conditional variance

• Textbook reading: 9.3, 9.5-9.6

• Course reader: 8.3-8.4

Mon–Fri, Nov. 23–27

Thanksgiving recess — no lectures, quiz, or tutorials

Mon, Nov. 30

Quiz 8

Inequalities and limit theorems

Wed, Dec. 2

Lecture

• Inequalities

• Law of large numbers

• Central limit theorem

• Textbook reading: 10.1-10.3

• Course reader: 9.1-9.4

Fri, Dec. 4

Lecture

• Course review

Cumulative final exam

Wed, Dec. 9

Cumulative final exam, 3:30-6:30pm