Math 20: Probability

Summer 2016

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Homework assignments will be due on Wednesday and Friday of each week.
The schedule and assignments will be posted here.
Policy: Homework is due at the beginning of class on the day it is due. Late work is generally not accepted.

wk date reading topic homework / comments

June 24
Set Theory
Introduction, basic set theory. Please complete the survey and turn in tomorrow. Class is at 9:20am!
June 25 at 9:20 am
§ 1.2 Basic probability, equally likely outcomes. Proof assignment: The problem at the end of the Set Theory Handout is due today.
The first Problem Set can be found here (due Wednesday).
June 27
§ 3.1 Counting techniques, birthday problem.(Problem solving night, 7-9 pm, Kemeny 004). Proof assignment 2 is due on Friday.
If you are sitting in on this class, please send me an email ( so that I can add you to my email list.
June 29
§ 3.2Counting techniques. First problem set is due today (solutions). Proof assignment due on Friday.
July 1
Binomial distribution and independence. The proof assignment is due today.
July 4
No classI will have office hours at the usual time today (4-5:30pm), and Tuesday (4-5pm).
I clarified the problem statment for Question 5 on Problem Set 2!
July 6
§ 4.1, 4.3 Conditional probability and independence. Problem set 2 due today (solutions). Proof assignment is due on Friday.
July 8
Conditional probability, apparent paradoxes, applications. Proof assignment 3 is due today.
The third problem set is due on Wednesday.
Practice problems for quiz (not to turn in):
1.2 # 1, 7, 9, 11, 22(*), 23(*), 26, 31,
3.1 # 2, 4, 6, 7, 10, 13, 17
3.2 # 1, 8, 12, 22, 31, 35
4.1 # 1, 2, 3, 9, 14, 22, 26, 27, 29.
Solutions to the second problem set are posted.
Here is a Review Sheet.
July 11
§ 6.1 Expectation. Quiz on Tuesday during X-hour. I will extend office hours to 4-6 pm today, office hours tomorrow are cancelled because I will be away at a conference.
July 13
§ 6.1, 6.2 Expectation and variance. Problem set 3 is due today, (solutions). Proof Assignment 4 is due on Friday. Quiz Solutions. Problem Set 4 will be due on Wednesday.
July 15
§ 6.1, 6.2 Joint distributions, geometric distribution, negative binomial distribution.
July 18
§ 5.1 Coupon collecting, more distributions. My office hours will be extended to 3:30-5:30pm on Monday, office hours on Tuesday will be cancelled and rescheduled to Wednesday from 9:15-10:10am.
Problem set 4 is due on Wednesday (solutions to Problem set 4), I fixed a typo on the hint for problem 5.
Proof Assignment 5 will be due on Friday (solutions).
July 20
§ 5.1 Poisson distribution. The proof assignment is due on Friday. This is an evolving document of good probability questions: Midterm Review. The fifth Problem Set will be due Wednesday (solutions).
July 22
§ 8.1 Important inequalities.
July 25
§ 2.1, 2.2 Continuous probability: density functions and expectation. Problem set due on Wednesday, Midterm on Thursday from 7-9.
Here is a collection of previous exams, continuous probability questions will not be on the exam.
July 27
§ 6.3 Geometric probability problems and cumulative probability. Office hours added today from 4:15-5:30. Office hours Thursday from 2:30-3pm, we will not be working through problems during this time. Midterm exam Thursday (tomorrow) from 7-9pm (solutions).
July 29
§ 5.2 Expectation, variance and normal distribution. The sixth problem set is due on Wednesday, (solutions).
August 1
§ 8, 9 Law of Large Numbers and Central Limit Theorem.The sixth Proof Assignment is due on Friday, (solutions).
August 3
§ 5.2 Exponential distribution and Gamma distribution.The seventh problem set is due on Wednesday (solutions), Problem 11 is cancelled due to length of assignment. The second quiz is on Tuesday during X-hour, it will include all of the continuous techniques through sums of continuous random variables on Friday.
August 5
§ 7.2 Sums of random variables and examples.Here is a review sheet for Quiz 2. I will have office hours on Sunday night from 7-8pm in place of my normal office hours on Tuesday. Problem Solving session on Monday night 7-9 in Kemeny 004. Monday's office hours will be from 3:00-4:30pm.
August 8
§ Quiz on Tuesday (solutions). Wrapping up continuous distributions. Infinite variance and expectation. Cauchy distribution and Benford's law.
August 10
§ Puzzles! The proof assignment is due on Friday - have fun with it! (Typo caught and updated). Here is a link to a Forbes Article about Benford's Law in fraud detection.
August 12
§ 11.1, 11.2, 11.3 Markov processes, basic linear algebra.The last problem set will be due on Friday, August 19th (solutions). Here is a Maple file to help you get started: maple. Here is an explanation of how Benford's Law arises from scale invariance (it's pretty cool).
August 15
Randomness, Chaos and Patterns. Here is an evolving document of good problems, I will update it periodically in the next week.
August 17
§ 11.1, 11.2, 11.3 Markov chains, regular and ergodic.
August 19
§ 11.1, 11.2, 11.3 Gambler's ruin and absorbing states, game theory.The last proof assignment is due on Monday (or Wednesday, if needed).
August 22
Game theory. Office hours this week: Monday 4-5:30, Tuesday 4-5, Wednesday 1:30-2:30, Thursday 1-2:30, Friday 4-5.
August 24
Review Send me an email if you have any questions you want to be sure we talk about.
August 27
Final exam The final exam is from 8am - 11 am in Kemeny 008 (right next door).