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

1Friday,
June 24
Set Theory
Handout
Introduction, basic set theory. Please complete the survey and turn in tomorrow. Class is at 9:20am!
Saturday,
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).
2Monday,
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 (moorek@math.dartmouth.edu) so that I can add you to my email list.
Wednesday,
June 29
§ 3.2Counting techniques. First problem set is due today (solutions). Proof assignment due on Friday.
Friday,
July 1
Binomial distribution and independence. The proof assignment is due today.
3Monday,
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!
Wednesday,
July 6
§ 4.1, 4.3 Conditional probability and independence. Problem set 2 due today (solutions). Proof assignment is due on Friday.
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.
4Monday
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.
Wednesday
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.
Friday
July 15
§ 6.1, 6.2 Joint distributions, geometric distribution, negative binomial distribution.
5Monday
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).
Wednesday
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).
Friday
July 22
§ 8.1 Important inequalities.
6Monday
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.
Wednesday
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).
Friday
July 29
§ 5.2 Expectation, variance and normal distribution. The sixth problem set is due on Wednesday, (solutions).
7Monday
August 1
§ 8, 9 Law of Large Numbers and Central Limit Theorem.The sixth Proof Assignment is due on Friday, (solutions).
Wednesday
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.
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.
8Monday
August 8
§ Quiz on Tuesday (solutions). Wrapping up continuous distributions. Infinite variance and expectation. Cauchy distribution and Benford's law.
Wednesday
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.
Friday
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).
9Monday
August 15
Randomness, Chaos and Patterns. Here is an evolving document of good problems, I will update it periodically in the next week.
Wednesday
August 17
§ 11.1, 11.2, 11.3 Markov chains, regular and ergodic.
Friday
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).
10Monday
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.
Wednesday
August 24
Review Send me an email if you have any questions you want to be sure we talk about.
Saturday
August 27
Final exam The final exam is from 8am - 11 am in Kemeny 008 (right next door).