General Class Information


Thursday, June 7th:

I have posted solutions to the suggested revision problems, solutions to the practice final problems, and solutions to the final exam from the last time I taught this course.

Tuesday, June 5th:

I have posted suggested revision problems, practice final problems, and the final exam from the last time I taught this class.  Solutions coming soon.

Thursday May 31st:

I have posted model solutions to quiz 2 and quiz 3.

Friday May 25th:

There will be an in-class quizz on Thursday, May 31st as originally scheduled.

Wednesday May 23rd:

The take home quiz is still due at the start of class tomorrow.

There will also be an in-class quiz tomorrow.

Friday May 11th:

Quiz 2 has been moved to Tuesday, May 22nd. 

Tuesday May 8th:

7:35am - according to campus is open, and CLASS WILL MEET TODAY.

Sunday May 6th:

Model solutions for the midterm are posted

Tuesday May 1st:

solutions to midterm review problems are posted

solutions to the previous midterm are posted

Monday April 30th:

1. Office hours will be held on Tuesday (1st May) this week, and not on Thursday (3rd May).

2. Currently, I intend for class to be held tomorrow.  If I hear that access to campus is blocked, I will try to update this announcement.

Saturday April 28th:

For the midterm, you may bring one page of notes, 8.5x11, double sided.

Friday April 27th:

I have posted a set of midterm review questions (the circled ones in the document).  Please try to work through them carefully.  I will post solutions sometime next week.

Thursday April 26th:

I have posted a set of review notes and the midterm from last time I taught this class.  I will post solutions to this midterm early next week.  Please note that this midterm was considered difficult, and I will try to make this year's midterm more closely resemble the homework problems.

Wednesday April 11th:

Copies of the homework problems for those who have the alternative textbook are now available.

Tuesday April 3rd: 

- Sections and TA office hours will start next week (week beginning Monday, April 9th)

- I have a few add codes available.  I will be dealing with those who want to add at the end of the lecture on Tuesday, April 10th.


Lecture Times

Tuesday and Thursday, 9:50 - 11:25am, Baskin Auditorium 101


Robin Morris

email: rdm @ - please put "AMS 131" in the subject line

phone: email is preferred; (650) 669 7159 if desperate

Office: Baskin Engineering 361b

Office Hours: Thursdays 11:30am - 12:30pm, or by appointment


Sisi Song,

Arthur Lui,

Matt Heiner,

TA Office Hours are:

Sisi Song - Monday 3-4pm BE 312C/D

Arthur Lui - Tuesday 8:30-9:30am, BE 121

Matt Heiner - Wednesday 11am-noon, BE312C/D



01A - W 8:00-9:05am - Matt Heiner

01B - W 9:20-10:25am - Matt Heiner

01C - Th 8:30-9:35am - Arthur Lui

01D - F 12:00-1:05pm - Sisi Song

All Sections will be in Engineering 2, Room 194

Modified Supplemental Instruction (MSI)

The MSI instructor this quarter is Shiva Ashok,  Meeting times are

Monday 12:00 - 1:00 PM, ARCenter 202
Tuesday 11:40 - 12:40 PM, Crown 104
Wednesday 2:40 - 3:40 PM, ARCenter 202
Thursday 5:20 - 6:20 PM, Porter 250

Discussion Forum

We will be using Piazza as the discussion forum for this class.


The main course text will be

"Introduction to Probability", J.K. Blitzstein and J. Hwang.

An alternate text is

Probability and Statistics, DeGroot and Schervish, 4th Edition, Pearson (2002)

Both texts cover the course material, but not in the same order.  We will be following Blitzstein and Hwang more closely.  If you plan on taking AMS 132, you should consider DeGroot and Schervish.


The proposed schedule is below.  Past experience is that this will change as the quarter progresses.  Subjects in strikethrough are those most likely to not be covered if time is short.

Date Topic DG&S B&H Homework  Lecture Notes
Tue April 3rd

Introduction; 3 views of probability; sample spaces; naive definition;

counting; axioms of probability

 1.1-1.8  1.2, 1.3, 1.6

 Section 1.9,


1, 2, 5, 8, 21, 22, 27, 29, 33, 42, 43

Th April 5th  Review of math pre-requisites       notes
Tu April 10th

Birthday problem; properties of probability; inclusion-exclusion;

matching problem; independence; conditional probability; Bayes' rule



 1.4, 1.6

2.5, 2.1, 2.3

 Section 1.9

Questions 45, 48, 51

We did not cover independence, conditional probability or Bayes rule.  We will cover these topics on Thursday.


Th April 12th

Law of total probability; conditional probability examples; 

conditional independence; Monty Hall problem; Simpson's Paradox.

2.1, 2.3


 2.3, 2.7


 Chapter 2,

Questions 1, 2, 5, 6, 11, 30, 35

We did not cover the Monty Hall problem or Simpsons' Paradox.  Please read the relevant sections of the textbook.


Tu April 17th

Gambler's ruin; random variables; Bernouli; Binomial; Hypergeometric;


2.4, 3.1


 2.7, 3.1, 3.3

3.4, 3.6, 3.2

 Chapter 2,

Questions 42, 47, 51

Chapter 3, Question 2

We did not cover the Hypergeometric distribution.  We will do that next time.


Th April 19th

Independence; Geometric distribution; expected values; indicator RVs;

linearity; Negative Binomial; examples


2.2, 5.5

4.1, 4.2 

 3.8, 4.3, 4.1

4.4, 4.2

Chapter 3, Questions 5, 9, 10, 21, 40, 42


We covered Hypergeometric, CDFs, PMFs from last time, and the quiz.

This means that we're running about a class behind the schedule here.  This is typical, and we'll adjust as we go along.


quiz (with solutions)

Tu April 24th

Poisson distribution; Poisson approximation; discrete vs. continuous;

PDFs; variance; standard deviation; Uniform distribution; universality

3.1, 3.2,


3.3, 4.3, 5.4 

 4.7, 4.8, 5.1

4.6, 5.2, 5.3

Chapter 3, Questions 40, 42

Chapter 4, Questions 3, 8 (parts a and c), 16 (part a), 20 (parts a and b), 22, 24, 30, 34

Again, we're about a class behind the schedule.



Th April 26th

Standard Normal Distribution; Normal normalizing constant;

Normal distribution; standardization; Law of the unconscious statistician

5.6, 4.1   5.4, 4.5  

We're still a class behind.


Tu May 1st

Midterm Review      


(previous review notes)

practice midterm questions -- these are taken from D&S.  They are the circled ones in the linked document.

1.12 Q 3, 4, 6, 9

2.5 Q 3, 5, 13, 16, 20, 23, 28

3.11 Q 1, 4, 9

4.1 Q 7

4.3 Q 9

4.9 Q 4

5.11 Q 5, 11, 12, 13, 18, 20

solutions to the practice midterm questions

previous midterm (note that this midterm was more difficult than anticipated)

solutions to the previous midterm

I will post solutions next week, after you have had a chance to try the problems for yourselves.

Th May 3rd

Midterm Exam (in class)      

 You can bring one page of notes, 8.5x11, double sided

Model Solutions

Tu May 8th

Exponential distribution; memoryless property; MGFs;

Bayes rule; Laplace's rule of succession

5.7, 4.4 




Today we covered the Normal Distribution.


Th May 10th

Use of MGFs; moments of Exponential and Normal; Sums of Poissons;

joint, conditional and marginal distributions; 2-D LOTUS; examples

4.4, 5.6


 6.5, 6.6

7.1, 7.2

 Chaper 4, Q 1, 2, 16(b), 57, 60

Chapter 5, 1(a), 5, 10, 22, 24, 25, 31, 36

Chapter 8, 4, 6, 11

 Today we covered the General Normal Distribution; the proof of the law of the unconcious statistician; transformations


Tu May 15th

Expected distance between Normals; Multinomial; Cauchy; covariance;

correlation; variance of a sum; variance of Hypergeometric 

1.9, 4.1

4.6, 5.3 

 7.3, 7.4  Chapter 8, 21, 22, 23, 26(a-d)

Today we covered more on transformations.  Convolutions (sums of RVs).  Bayes Rule and Laplace's rule of succession.


Th May 17th

Transformations; Log Normal; convolutions; Beta distribution;

Bayes' Billiards


5.6, 5.8

3.8, 3.9 

 8, 8.2


 Chapter 8, 29, 40

Today we covered more on using Bayes Theorem, and the Beta distribution. 


Note that Quiz 2 has been rescheduled and will be held on Tuesday, May 22nd

Tu May 22nd

Gamma distribution; Poisson process; Beta-Gamma; order statistics;

conditional expectation



5.7, 5.4

7.8, 4.7 

 5.6, 8.4

8.5, 8.6, 9

 Chapter 7, Q 1, 2, 6, 7, 16, 31

Today we covered joint, marginal and conditional distributions for continuous random variables; 2D LOTUS; Covariance and the variance of a sum of random variables.


quiz 2 with solutions


Th May 24th

Conditional expectation (cont);waiting times  4.7   9.1  Ch 7, Q 39, 40, 49


Today we continued with covariance and correlation and the covariance of independent and non-independent random variables.


Tu May 29th

Sum of random number of RVs; Inequalities; 

Law of large numbers; central limit theorem


 10, 10.2



Ch 7, Q 72, 73

Ch 10, Q 1, 17


Today we covered the multivariate normal and the bivariate normal; the Law of Large Numbers and the inequalities used in proving the Weak LLN.

As I mentioned in class, I had a missing negative sign in the derivation of the conditional distribution of one variable in the bivariate normal.  This is corrected in the notes.



Th May 31st

Chi-squared; Student-t; multivariate normal;

Markov chains; transition matrix; stationary distribution


8.2, 8.4

5.10, 3.10 

 10.4, 7.5

11, 11.1, 11.3

 Ch 10, Q7, 18, 21

Today we covered more inequalities, and the central limit theorem.


quiz 3 with solutions


Tu June 5th

Markov chains (cont). 3.10     Ch 11, Q4  

Th June 7th



Suggested revision problems - see this document, and look at problems

1.12 Q 4, 11

2.5 Q 2, 5, 17, 20, 21, 24, 26, 36

3.11 Q 4, 5, 8, 10, 16, 21, 27, 28, 29

4.9 Q 5, 8, 11, 14, 22

5.11 Q 7, 8, 12, 20

6.5 Q 9, 10, 12

solutions to the suggested revision problems

Also, some practice final questions

solutions to the practice final questions

And the final exam from when I last taught this class.  Note that there is a typo in question 1.  It should read



solutions to the final from last time


Solutions will be posted soon are now posted.

Wed June 13th

Final Exam, noon-3pm, Baskin Auditorium


      solutions to the final

Additional Information


UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter. At this time, I would also like us to discuss ways we can ensure your full participation in the course. I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089, or by email at

Academic Integrity

You are reminded of the University's Policy on Academic Integrity.  I hope not to have to remind any of you individually about this policy.

Some Thoughts About Lectures

"In Praise of Lectures" gives some ideas about the purpose of lectures, note-taking, and not being afraid to ask questions. It's target audience is more advanced mathematics students, but everything it says applies here. Think about the ideas it presents, and you will have a better time in AMS7 lectures. In particular

  • Lectures complement reading the textbook. In lectures I can spend extra time explaining ideas that students find confusing or difficult. I can try to judge from your behaviour your level of comprehension and adjust what I say accordingly.
  • I am not, however, a mind-reader. If you have questions, please ask them. If you don't understand something, chances are there are others who don't understand either, but are more inhibited than you are.
  • If you don't want to concentrate on the lecture, you're not required to attend. Please be considerate of those who do want to concentrate.
  • The lectures will present the material, but you will only know if you truly understand it if you try the homework problems. Only by applying the ideas yourself will you know that you have mastered them. “I went to a lecture on the violin, but when I tried playing one it sounded horrid. The lecturer can't have been any good.”
  • If you are having difficulties, please come and see me during office hours. Do this early in the quarter, rather than a week before the final exam. My goal is for everyone to understand and be comfortable with the material. If this is also your goal, I'm willing to do what's needed to help you achieve that goal.