# Statistics 430: Introduction to Probability

## 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

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

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