Statistics 430: Introduction to Probability

Spring Semester, 2003

Prof. Robert Stine
444 Huntsman Hall

Announcements

If you would like to see the final exam from last year's class, you can get it here --- albeit without --solutions! For those, visit the TA or send me a question. As with the other exams from last year that you have seen, the course this year is a bit different, so you can expect the exam to be different as well.
The TA for the class, Linxu, will have extra office hours 1-5pm on Wednesday, Apr. 30th. I will be around Tuesday and Thurs afternoons from 3-5 as before.
In case you did not know, the Statistics Department offers help through its Stat Lab located in 462 Huntsman Hall. This resource offers help for all of our courses. The person staffing the Stat Lab will not likely be familiar with what we have been doing in class, but will be able to help you with questions about the material and assignments.
Some have expressed "curiosity" about their standing in this class. I won't talk about letter grades yet, but here are the scores on the material to date:
- HW 1: mean 9.2, sd 0.9
- HW 2: 9.0, 1.1
- HW 3: 9.3, 1.0
- HW 4: 8.3, 1.3
- HW 5: 9.2, 0.9
- HW 6: 9.3, 0.8
- HW 7: 9.6, 0.9
- HW 8: 8.6, 1.2
- HW 9: 8.8, 1.0
- MT 1: 83, 9
- MT 2: 74, 14

Syllabus

The following list of class topics and test dates is approximate and is offered as a guide. I will adjust the syllabus as suits the speed that we cover the material, so do not be too surprised by changes. The dates for the two in-class tests are not yet fixed (as of Jan 10), but will become fixed soon after the first class.

All of the section numbers given here refer to the required text

A First Course in Probability (Sixth Edition) (2002), by S. Ross

Assigned problems are listed by chapter number; for example, 9.3 is problem number 3 from Chapter 9. Questions from the "theoretical" group are denoted with a "t", as in t9.3. You should be able to do the problems after the lecture where they are listed on the syllabus. Assigned problems will be collected one week later in class and graded.

Date	Class Topic	Read Sections	Assignment
Tues, Jan 14	Probability, sets, and counting	1.1-1.5, 2.1-2.3
Thur, Jan 16	Manipulating probabilities	Sections 2.3-2.5	A1: 2.2,5,8,9,15ac,18,23,27,37,45 (soln)
Tues, Jan 21	Conditional probability	3.1-3.3
Thur, Jan 23	Bayes rule	3.1-3.3	A2: 3.8,11,16,19,26,33,37,43,49,54 (soln)
Tues, Jan 28	Independence	3.4
Thur, Jan 30	Review	Chapters 1-3	Review problems.
Tues, Feb 4	Test (in class, closed book, one sheet)	Chapters 1-3
Thur, Feb 6	Random variables	4.1-4.2, 4.9	A3: 4.5,6,11,18,20,21,27,30,35,38 (soln)
Tues, Feb 11	Expected value and variance	4.3-4.5
Thur, Feb 13	Chebyshev's inequality	4.5, 8.2	A4: 4.46,51,60,61,67,68,70,77; 8.2,8.4a (soln)
Tues, Feb 18	Binomial, Poisson, & geometric	4.6-4.8.2
Thur, Feb 20	Sums of r.v.s: Chebyshev again	8.2, 8.3	A5: 4.32,33,42,t9,t25; 8.19,20,22ab,t6a (soln)
Tues, Feb 25	Poisson process (clumping handout)	4.7, 9.1
Thur, Feb 27	Exponential r.v.	5.1-5.2, 5.5	Review problems
Tues, Mar 4	Review	Chapter 4-7.1
Thur, Mar 6	Test (in class, closed book, two sheets)	Chap 4, 8.2, 9.1
Mar 10-14	Spring Break	Sure
Tues, Mar 18	Exponentials and gamma	5.1-5.3, 5.5, 5.6.1
Thur, Mar 20	Normality	5.4	A6: 5.2,5,8,13,15,21,26,30,34,39
Tues, Mar 25	Central limit theorem	5.4, 8.3
Thur, Mar 27	Joint discrete variables	6.1-6.4	A7: Assignment
Tues, Apr 1	Covariance ( data )	6.4, 7.3
Thur, Apr 3	More covariance	7.3	A8: Assignment
Tues, Apr 8	Conditional distributions, expectation	7.4-7.5
Thur, Apr 10	Applications of conditional expectation	7.4-7.5	A9: 7.9,12,19,34a,36,46,48,53,55,68 (soln)
Tues, Apr 15	Introduction to Markov chains	9.1-9.2
Thur, Apr 17	Review homework, Markov chains	9.1-9.2	A10: 9.4,8,9,10
Tues, Apr 22	Markov chains	9.1-9.2
Thur, Apr 24	Wrap-up	Chapters 1-9
Monday, May 5 11am-1pm	Final exam (closed book, 3 sheets) Steinberg-Dietrich 350

Grades

Your grades will be determined as the following weighted average of your scores:

30% Assignments
Generally one assignment will be due every week or two.
30% Two in-class tests
40% Final exam (May 5)

Some Related Links

Markov chains and Monopoly: Need to improve your Monopoly style of play. This site uses a Markov chain to model this board game.
Tossing the Euro coin: Rumor has it that the Euro is a 'biased coin' that tends to land more on one side than the other. Other research looks at how coins from different countries migrate around the EU
Bayes and Google: Turns out that a lot of the web traveling strategy used by the Google search engine utilizes Bayes method -- but in a very big way.

Teaching Assistant and Office Hours

The teaching assistant for this class is Linxu Liu ( linxu@wharton.upenn.edu ). He staffs the Stat Lab (462 JMHH) from 11am-1pm on Mondays. He has additional office hours reserved for Stat 430 on Monday from 3pm-5pm. His office is 431.3 in Huntsman Hall.

In addition, I will have office hours on Tuesday following class from 3-5 and Thursday following class from 3-4. If you need to see me outside these times, please send me an email ( stine@wharton ). I am generally around quite a bit, but please send me a note to set up a time.