University of Califonia,

Los Angeles

This is the course website for Math 170A: Probability Theory running in Fall 2017. All information about homework, quizes and exams will be posted here.

The syllabus contains information on the official policies for collaboration on homework, late homework, grading and changing grades.

We will be using Piazza for this class. See below for more information.

Instructor: |
Noah White (noah@math.ucla.edu) |

Office hours: |
MS 6304, Thursday 10-11:30am, Friday 9:30-11am |

TA: |
Robbie Housden (rhousden@math.ucla.edu) |

Office hours: |
MS 3915B, Monday 2-3pm, Tuesday 8:30-9:30am, Wednesday 2-3pm |

Please check back here as office hours and locations may change. I am teaching two classes this quarter. To accommodate all students, I am going to prioritise 3B on Thursdays and 170A on Fridays. Feel free to come to either office hour with this in mind.

I would appreciate your help managing communication for the class.

Mathematical questions should be asked on Piazza (see below). In addition you should make use of my, and the TA’s, office hours. Administrative questions should in the first instance be directed to your TA. If your TA cannot resolve your query then you should contact me.

If you need to email me, the subject line **must** include the string `math170a`

. If not, then there is a good chance your email will slip through the cracks and remain unanswered.

Introduction to Probability by D. P. Bertsekas and John N. Tsitsiklis

Owning a copy of the textbook will be very helpful and is recommended however you might not find it necessary. I will post links to other sources here as time goes on. Feel free to buy an old or used copy of the textbook, it wont be necessary to own the second edition.

There will be a problem set assigned every week. Most of these will not be collected however it is strongly recommended that you complete it. Questions are drawn from the textbook and from the supplementary problems which can be found below.

In weeks 2, 5, 9 (as indicated in the class schedule below) a small number questions from the problem sets will be assigned as homework and collected and graded.

In weeks 3, 6, 10 a quiz will be conducted in the discussion section. Questions on the quiz will be drawn from the problem set (or will be very similar to one of these questions). The lowest 2 scores out of all homeworks and quizzes will be dropped. The homework and quizzes will count for a total of 10% of your grade.

- Problem set 1
- Problem set 2 (solutions) (HW1: problems 4 and 6.)
- Problem set 3
- Problem set 4
- Problem set 5 (HW2: problems 3 and 4.)
- Problem set 6
- Problem set 7
- Problem set 8
- Problem set 9 (HW3: problems 8 (supp problems) and 5.)

Here I will indicate which sections of the textbook will be covered in each lecture and the relevant problems in each problem set. It is recommended that you read the textbook and think about some of the problems **before** the lecture.

- Lecture 1: Sets and manipulating sets.
- Lecture 2: Sample spaces.
- Lecture 3: Probability laws.
- Lecture 4: Counting.
- Lecture 5: More counting and conditional probability.
- Lecture 6: Conditional probability.
- Lecture 7: Baye’s rule.
- Lecture 8: More Baye’s rule and ndependant events.
- Lecture 9: Independant events.
- Lecture 10: Review
- Lecture 11: Random variables and PMFs.
- Lecture 12: More PMFs.
- Lecture 13: Functions of random variables.
- Lecture 14: Expectation and mean.
- Lecture 15: Variance.
- Lecture 16: Joint PMFs.
- Lecture 17: Covariance and conditioning.
- Lecture 18: More conditioning and independence.
- Lecture 19: More independence.
- Lecture 20: Review.
- Lecture 21: Continuous random variables.
- Lecture 22: Probability density functions.
- Lecture 23: Normal random variables.
- Lecture 24: Conditioning.
- Lecture 25: Coninuous Bayes.
- Lecture 26: Review.
- Lecture 27: Review.

There will be two midterms and a final exam. Apart from the exceptions mentioned below, only writing equipment will be allowed in exams. Exams must be written in pen.

**Midterm 1:**12pm Monday 23 October**Midterm 2:**12pm Monday 20 November**Final Exam:**3pm Friday 15 December

**Cheatsheets:** For each exam, students may bring a cheat sheet. Each student must prepare their own handwritten cheat sheet. For the midterms, the cheat sheet may consist of one side of half a standard (A4 or letter) sheet of paper (i.e. A5 or letter folded in half lengthways). For the final, the cheat sheet may consist of one side of a standard sheet of paper. Cheatsheets that do not meet these requirements will be confiscated at the beginning of the exam.

**Calculators:** You may use a non-programmable, non-graphing calculator in exams. Calculators not meeting this specification will be confiscated.

**Study:** Here I will post some practice exams which might aid your study.

The midterm scores will be adjusted to account for any difference in difficulty. Your final grade will be calculated using the maximum of the following two grading schemes. Your letter grade will then be determined by your rank in the class. Unless something very out of the ordinary occurs I expect to give approximately 30-40% A’s and 60-75% A’s and B’s combined.

Option 1:

```
10% (4 best homework/quiz scores) +
40% (combined midterm scores) +
50% (final exam score)
= raw final grade
```

Option 2:

```
10% (4 best homework/quiz scores) +
30% (best midterm score) +
60% (final exam score)
= raw final grade
```

Effectively, this will mean that unless you score worse in the final than both midterms, your **lowest midterm score will be dropped**. This also means missing one midterm probably will not impact your grade in any serious way.

This is a tentative schedule. Apart from the dates of exams, it may change. Numbers refer to sections of the textbook.

Monday | Tuesday | Wednesday | Thursday | Friday | |
---|---|---|---|---|---|

0. | 9/25 |
9/26 |
9/27 |
9/28 |
9/2911.1 |

1. | 10/221.2 |
10/3 |
10/431.2 |
10/5 |
10/641.3 |

2. | 10/951.3 |
10/10 |
10/1161.4 |
10/12 |
10/1371.5 HW 1 |

3. | 10/1681.5 |
10/17 Quiz 1 |
10/1891.6 |
10/19 |
10/2010Review |

4. | 10/23 Midterm 1 |
10/24 |
10/25112.1 |
10/26 |
10/27122.2 |

5. | 10/30132.3 |
10/31 |
11/1142.4 |
11/2 |
11/3152.5 & 4.2 HW 2 |

6. | 11/6162.6 |
11/7 Quiz 2 |
11/8172.6 |
11/9 |
Vets Day(no class) |

7. | 11/13182.7 |
11/14 |
11/15192.7 |
11/16 |
11/1720Review |

8. | 11/20 Midterm 2 |
11/21 |
11/22213.1 |
Thanksgiving(no class) |
Thanksgiving(no class) |

9. | 11/27223.1 |
11/28 |
11/29233.2 |
11/30 |
12/1243.3 HW 3 |

10. | 12/4253.4 |
12/5 Quiz 3 |
12/6263.5 |
12/7 |
12/8273.6 |

Piazza is a question and answer style forum which we will be using for this class.

You can ask questions, either as yourself or anonymously. I highly encourage you to also try answering others’ questions. Teaching others is by far the most effective way to learn and solidify what you already know. The TAs and I will monitor the discussion and answer questions occasionally.

Obviously homework questions and solutions should not be posted on Piazza. Offences will be treated as academic dishonesty/cheating.