STAT 511 (Probability)

### Instructor

David Hitchcock, associate professor of statistics

### Syllabus

Syllabus: (Word document) or (pdf document)

### Office Hours -- Fall 2013

MWF 10:45-11:45 a.m., Tues 11:00-12:00, Thur 10:00-11:00 a.m., or please feel free to make an appointment to see me at other times.

Office: 209A LeConte College
Phone: 777-5346
E-mail: hitchcock@stat.sc.edu

### Class Meeting Time

MWF 9:40 a.m.- 10:30 a.m., LC 210A

### Current Textbook

Mathematical Statistics with Applications, 7th edition. (2008), by Wackerly, D., Mendenhall, W., and Scheaffer, R.

### Course Description

511—Probability [=MATH 511] (3) (Prereq: MATH 241 with a grade of C or higher) Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities; moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate and bivariate normal distributions.

Purpose: To provide a strong foundation in basic probability for understanding the concepts and modelling of random phenomena, and to prepare students for study of the mathematical development of statistical methodology.

### Course Notes

You are encouraged to print out these notes ahead of time and bring them to class.

### Homework

Note: Problems in the first column will be graded on effort and correctness (1 point for making a decent effort at the problem, 1 point for a correct (or very nearly correct) solution).
Problems in the second column will be graded on effort (1 point for making a decent effort at the problem) and not for correctness,
but you should try to understand how to solve all these problems before test time!

You must write your homework solutions NEATLY. You must present your solutions in the order that the problems are assigned (with the Column 2 problems last).
Handwritten solutions are fine, but if you type solutions, you should use either LaTeX or MS Word's Equation Editor,
since other word processors (like Word without Equation Editor) are not designed for mathematical typing.

NOTE: Some of the problem numbers in the "International Edition" of the textbook are switched around from the regular edition. If you have the international edition, you SHOULD compare problem numbers with me or with a classmate who has the regular edition to make sure you're doing the problems assigned.
The problem numbers given below reflect the regular 7th edition.

 Due Date Problems to be Graded on Effort and Correctness Problems to be Graded Solely on Effort Friday, August 30 2.1, 2.2, 2.6(b), 2.8 2.144 Monday, September 9 2.14, 2.18, 2.25, 2.34, 2.42, 2.71[show work!] 2.20, 2.54, 2.56, 2.60, 2.61 Monday, September 16 2.72, 2.81, 2.94, 2.116, 2.124 2.76, 2.82, 2.100, 2.101, 2.110, 2.128 Wednesday, October 2 3.6, 3.12, 3.22, 3.34, 3.40, 3.72, 3.73, 3.74, 3.96(a), 3.110 3.30, 3.32[assume E(Y)>0], 3.58, 3.77, 3.120[use trial-and-error to maximize] Thursday, October 10 by 4 p.m. 3.122, 3.134, 3.145[use binomial expansion], 3.146, 3.150, 4.1, 4.14(a,b,c) 3.124, 3.126, 3.156, 3.158, 3.159, 3.196, 4.8(a), 4.20, 4.30 Wednesday, October 30 4.38(a), 4.48, 4.58(a,b,c,d,e), 4.74(a,b,c), 4.142(a,b)[use table on p. 838 for (a)] 4.38(b), 4.50, 4.62, 4.74(d), 4.76, 4.136(a) Wednesday, November 13 4.82, 4.88, 4.94, 4.96(a,b,c), 4.110, 4.134(a,b), 4.146, 4.155(show work!), 4.158 4.81, 4.99[use R (or integrate by parts) for (b)], 4.106(a), 4.124(a)[note 40% = 0.40], 4.154(a,b), 4.156, 4.157[also find P(X < 150)] Tuesday, December 3 by 4 p.m. 5.3, 5.16(a), 5.22, 5.26[for (b), use definition of conditional probability], 5.49, 5.52, 5.74(a,b,c), 5.91 5.4, 5.8(a,c), 5.12(a), 5.48, 5.80, 5.92, 5.97

### Some Practice Problems from the Last Few Sections

5.103 [For simpler problems, show that: V(3Y_1 + 4Y_2) = 156, V(3Y_1 - 6Y_3) = 360, cov(3Y_1 + 4Y_2, 4Y_2 - 6Y_3) = 126],
5.123, 5.125(a), 5.135

Answers to these problems are given in the back of the book.

### Formula Sheets

• Test 1 Formula Sheet (You do NOT have to bring this to the test. A copy will be provided to you with your test.)
• Test 2 Formula Sheet (You do NOT have to bring this to the test. A copy will be provided to you with your test.)
• Test 3 Formula Sheet (You do NOT have to bring this to the test. A copy will be provided to you with your test.)

### Exams

• Exam 1: September 18
• Exam 2: October 16
• Exam 3: November 20
• Final Exam: Saturday, December 14 - 9:00 a.m.