STAT 310/ECON 382: Probability and Statistics

Rice University, Spring 2005

Instructor: Clay Scott
Classroom: Duncan Hall 1070
Office: Duncan Hall 2077
Campus extension: 2695
Email: cscott
Office hours: by appointment

Announcements

• Final exam stats: the first, second, and third quartiles were 69, 85, and 96.5, respectively. These numbers are percentages out of 100.
• You can pick up your graded final if you can find me in my office.
• I will hold all unclaimed material from the course in my office through next semester.

Course assistants

Class Notes

I make no guarantees about the accuracy or legibility of these notes. Often I/we find mistakes before or after I present the material, and sometimes I present things in a different order. On the other hand, sometimes I don't write everything from my notes on the board, so you may find some additional comments from time to time. These are here simply as a convenenience to those who find them useful.

• Intro, set theory, axioms
• Counting
• Ordered versus unordered outcomes; the dice example and follow-up to previous lecture
• Conditional probability
• Independent events and Bayes' theorem
• Discrete Random Variables
• Common discrete RVs, expectation, MGFs.
• Continuos RV, pdfs, cdfs, uniform and exponential families, percentiles
• The gamma and chi-square distributions, upper percentiles
• The normal distribution
• Functions of a random variable, distribution function technique, change of variable technique, lognormal and Cauchy distributions.

• Multivariate distributions, joint pdfs/pmfs, marginals, independence, sums of independent random variables
• Sampling distributions
• Functions of a normal random sample
• Estimation theory, maximum likelihood, unbiased estimators
• Confidence intervals for means, variance known
• Confidence intervals for means, variance unknown
• Hypothesis testing, testing the mean (known/unknown variance)
• The central limit theorem
• Tests about proportions
• Chi-square tests
• Review*

*To clarify the last page of the review: Based on what we have covered in lectures/homeworks, I think you should be prepared for all questions on the final. The recommended reading will give you additional examples of how the principles we have developed can be applied.

Textbook

Hogg and Tanis, Probability and Statistical Inference, 6th Ed.

Prerequisites

Calculus at the level of Math 102.

Topics to be covered

Hogg and Tanis, Chapters 2-8.

Final Grade

Within each letter grade I may also assign a (-) or (+)

Since the percentages add to 105, this effectively allows you to skip/drop about two homeworks. The extra 5% are available as extra credit. I do this because it is easier than giving extensions for homeworks on a case-by-case basis.

I may curve the final grades up (to your benefit) if it seems appropriate to me.

Homework Policy

Homeworks will be due at the beginning of class on Tuesdays and returned on Thursdays. Homework handed in late but before 5 pm the following day will be penalized 20%. Homework handed in later than 5 pm on the day after the due date will not be accepted. Please hand in late homework to one of the graders, not me.

Homeworks answers that are difficult to read or comprehend will receive little to no credit. Correct answers that lack clear justification (unless the problem is trivial) will receive little to no credit.

Exams

Both midterms will be in class and last for one class period. I have not yet determined the format of the final. All exams will be closed book and closed notes but you will be allowed to prepare a cheat sheet. You must hand-write your own cheat sheets. You may not type or photocopy them. If you must miss a midterm, please notify me as soon as possible to make other arrangements.

Homeworks

Homeworks will be assigned and collected on Thursdays unless otherwise indicated. Homework problems will be posted here as they are assigned. All problems (unless otherwise noted) are from the book.

Homework Solutions

Have been taken down

Problem Sessions

There will be a weekly problem session lead by a teaching assistant to help you with the homework. This will take place every Monday evening from 5:15 to 7 PM in Duncan Hall 1042. I will instruct the TA to give suggestions but not answers. Be aware that the TA may leave early if no one shows up.

Collaboration and the Honor Code

You will derive the most benefit from the homeworks if you work on them by yourself before discussing with others. You may work together on homeworks, but you are required to write up your solutions by yourself. Your solutions should be distinct from your classmates'. You may not refer to material from previous offerings of this course, including problem sets and solution sets. If you find a solution to a problem anywhere (with the exception of the back of the book for odd-numbered problems), you may not use it.

Students with Disabilities

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disabled Student Services in the Ley Student Center.