### Math 3355 Probability

Time and place: TTh 10:40-12:00, Room 211, Tureaud Hall.

Instructor: James Madden, 213 Prescott Hall, madden@math.lsu.edu, (225)-978-3525 (cell). Office hours: TTh 9:00-10:30 or by appt.

Textbook: S. Ghahramani, Fundamentals of Probability.

Here is a guide that describes what to read up to the midterm.

Here is a guide that describes what you will be responsible for on the final.

Goal: Students will acquire a working knowledge of basic probability theory, including continuous random variables and the Central Limit Theorems.

Grading: Homework: at most 25%.  Weekly quizzes 25%.  Midterm and final at least 50%. The final is scheduled for Thursday, May 12, 7:30-9:30 AM.

week mm/dd D Topic Assignment Notes/resources

## A1

01/18 T
• Vocabulary of probability: experiments, outcomes, events, probability spaces.
• Discrete Probability Spaces
Do the problems in the notes. Lecture 1 | Mathematica Notebook 1
01/20 Th
• Tree diagrams
• New spaces from old
Do the problems in the notes. Do the exercises in Notebook 2. Lecture 2 | Mathematica Notebook 2 | Quiz 1

## A2

01/25 T Combinatorial methods --- Lecture 3
01/27 Th Examples (the hypergeometric distribution)

Textbook, pages 51-2: 3, 4, 12, 20, 21 and page 65: 20. (65:20 asks for the probabilities of all the poker hands. This is long.) Do the project in the lecture notes.

Quiz 2 | Lecture 4 | Mathematica Notebook 4 | Mathematica Notebook 4a (Contains solution to the project in the lecture notes.)

## A3

02/01 T Conditional Probability, Independence, Two-way tables. 3.1: 5, 9, 11, 13, 17
3.2: 1, 3, 5, 9
Ch.3rev: 8, 9, 11, 13
Lecture 5
Problems from the textbook:
3.1 | 3.2 | 3.3 | 3.4 | 3.5 | Ch.3rev
02/03 Th Bayes's Rule

3.3: 1, 4, 5, 7
3.4: 1, 2, 9, 11
Ch.3rev: 14, 15, 17

HAND IN February 8: 3.1:17 and the Homework problem in Lecture 6

Quiz 3 | Lecture 6 | Mathematica Notebook 6

## A4

02/08 T Random Variables Do the problems in the lecture notes. Lecture 7, 2nd edition (This was updated Feb. 9. If it looks thae same as the one you saw before, refresh the web page.)
Mathematica Notebook 7
02/10 Th More on Random Variables --- Quiz 4 | Lecture 8 | Mathematica Notebook 8

## A5

02/15 T Review Examples HAND IN on Tuesday, February 22: the "extension problems" in the Lecture 9 notes. Lecture 9
02/17 Th More examples HAND IN on Tuesday, February 22: problem 3.5:33 and extension a and b of problem 3.5:35in Lecture 10 notes. Quiz 5 | Lecture 10

## A6

02/22 T More on Expectation; Special Discrete Distributions --- Lecture 11
02/24 Th The Poisson Distribution --- Lecture 12 | Mathematica Notebook | Quiz 6

## A7

03/01 T Review Link to practice test and answers. Note: the midterm will cover more than this practice test. All homework is fair game. Solutions to Lect. 10 probs. | Mathematica Notebook on Lect. 9 probs.
03/03 Th Midterm Exam on all material up to an including Lecture 11 Here is a guide that describes what to read up to the midterm. ---

## --

03/08 T Holiday --- ---
03/10 Th Midterm postmortem --- Midterm Solutions

## B1

03/15 T Continuous Probability I. Read Chapter 6 Lecture 13
03/17 Th Continuous Probability II: Uniform distributon, Cauchy distribution, Expectation from CDF. Re-read Chapter 6 Lecture 14 | Quiz 7

## B2

03/22 T Transformations Page 245: 1, 3, 5, 7 Lecture 15 (The midsemester grades are available)
03/24 Th Transformations; expected value, variance, moments Page 254: 5, 9, 11, 17 Lecture 16 | Quiz 8

## B3

03/29 T The Normal Distribution Page 281: 5, 9, 11, 12, 15, 33 Lecture 17
03/31 Th The Exponential Distribution; adding random variables Do the last problem in the "quiz", and hand it in Monday. Do the last exercise in the lecture notes. Lecture 18 | "Quiz 9"

## B4

04/05 T Discrete Generating Functions (Chapter 11) Do the problems in the lecture Lecture 19
04/07 Th Bivariate distributions. Read Secion 8.1.
Do: Section 8.1: 2, 3, 9, 10, 11, 12
Lecture 20 | Quiz 10

## B5

04/12 T Sections 8.2, 8.3. Independence and conditional distributions --- Lecture 21 | Buffon-Demo (Mathematica)
04/14 Th Sections 8.4. Change of variables Do the review problems for Chapter 8 Lecture 22 | Quiz 11

## --

04/19 T Holiday --- ---
04/21 Th Holiday --- ---

## B6

04/26 T Expectation --- Lecture 23
04/28 Th review --- Notes for review

## B7

05/03 T Covariance --- Lecture 24
05/05 Th TBA --- ---