ST 720 Probability Theory (Spring `00)

Instructor:

Richard Davis , Dept of Statistics
102A Statistics, 1-7321
rdavis@stat.colostate.edu

 

Teaching Assistant:

Sarah Streett
305 Statistics, 1-3778
streett@stat.colostate.edu

 

Time:

MW: 11-11:50, 104D Eng

T: 4:10-5:00, 102D Eng

W: 4:10-5:00 005 STAT

R: 8:00-8:50 005 STAT

 

Office hours:

Catalog Description: 04(4-0-0). Measure theoretic probability, characteristic functions; convergence; laws of large numbers; central limit theorem, extreme values, asymptotic theory.

Prerequisite: ST 520 and M 517.

Required Text: A Probability Path, by S. Resnick, Birkhäuser, Boston

• Billingsley, P. Probability and Measure, 3rd edition
• Breiman, L. Probability
• Chung, K.L. A Course in Probability Theory
• Doob, J.L. Stochastic Processes
• Loeve, M. Probability Theory
• Feller, W. Introduction to Probability Theory and Its Applications, Vol 1 & Vol 2
• Shiryayev, S. Probability

 

Topics to be Covered in Resnick:

Chapters 1-9, and parts of 10 (10.1-10.5) time permitting.

Midterm Schedule:

Midterm 1: February 24, 3-5:00 or 4-6:00. (Covers through Chapter 4)

Midterm 2: April 12, 3-6:00 or 4-7:00. (Covers Chapters 1-6)

 

Final Exam: May 8; 9-12:00 (Rm 005 STAT)

 

Course Assignments:

HW 1 (Due 1-26) p20-27: 1, 3, 5, 8, 12, 14, 15, 16, 18, 20, 21, 22, 27

HW 2 (Due 2-2) p20-27: 17, 24, 29, 30, 31, 34, 35, 41, 42; p63: 1, 2, 5, 11, 16

HW 3 (Due 2-9) p63-: 3, 6, 8, 11, 12, 13, 14, 22; p85: 2, 3, 4, 7, 8

HW 4 (Due 2-16) p85: 6, 9, 11, 12, 13, 15, 19, 20, 25; p110: 1, 4, 5

HW 5 (Due 2-23) p110-: 6, 7, 8, 9, 10

HW 6 (Due 3-15) p110-: 13, 16, 17, 18, 19, 21, 25, 26, 28

HW 7 (Due 3-22) p110-: 23; p155: 3, 6, 7, 8, 13, 29

HW 8 (Due 3-29) p155: 15, 16, 23, 24, 30, 36, 37, 38

HW 9 (Due 4-5) Show X_n \to X a.s. iff for every \epsilon>0, P(|X_n-X| > \epsilon, i.o.) = 0.

p.155: 5, 9, 11, 19, 22; p.195: 1(a-c), 12, 13, 14

HW 10 (Due 4-19) p.196: 3, 5, 11 a,b,c,e, 31, 33; p.234: 4,6

HW 11 (Due 4-26) p.234: 8, 11, 13, 14, 15; p.282: 1, 5b, 7, 10

HW 12 (Due 5-3) p.282: 12, 13, 20, 36; p.321: 2, 6, 10, 16, 32

Grading:

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