STAT25300/STAT31700 WINTER 2013

STAT253/317 Winter 2013
Introduction to Probability Models

Class Meeting: MWF 11:30-12:20 am, Eck117

NameOfficeTelephoneE-mailOffice Hours
Instructor Yibi Wed 4-5pm in Eck104A or by appointment
CARishideep RoyRyerson N375773-834-3393 rishideep@galton.uchicago.eduTuTh 4:30-5:30 in Eck117 or by appointment

Textbook: Introduction to Probability Models (2010, 10th edition) by S. Ross.[IPM10e]

Complete Syllabus: Click Here

Course Schedule

DateTopicsHomework (Solutions are on Chalk)
M Jan. 07 Lecture 1: definitions of Markov chains, transition probabilities, Ehrenfest diffusion models, discrete queueing models, Sections 4.1 HW1Jan7.pdf
WJan. 09 Lecture 2: Chapman-Kolmogorov Equation. Sections 4.2 HW2Jan9.pdf
FJan. 11 Lecture 3: classification of states (recurrent, transient), recurrence and transience of simple random walks. Section 4.3, p.204-210 HW3: Exercise 4.13, 4.14 on p.277, due Fri, Jan. 18
M Jan. 14 Lecture 4: Limiting distribution I. Sections 4.4No Assignment
WJan. 16 Lecture 5: Limiting distribution II. Sections 4.4.HW4Jan16.pdf
FJan. 18 Lecture 6: backward Markov chain, time reversibility, detailed balanced equation. Sections 4.8HW5Jan18.pdf
M Jan. 21Martin Luther Kings' Day, No Class
WJan. 23 Lecture 7: Branching Processes. Sections 4.7.HW6Jan23.pdf
FJan. 25 Lecture 8: Generating FunctionsHW7Jan25.pdf
M Jan. 28 Lecture 9: exponential distributions, memoryless property, definitions of Poisson processes. Reading: Section 5.1-5.3
HW8: Exercise 5.20, 5.22 on p.357 due Mon Feb. 4
WJan. 30 Lecture 10: interarrival times of a Poisson process, conditional distribution of interarrival times. Sections 5.3.HW9Jan30.pdf
FFeb. 1 Lecture 11: thinning, superposition, "converse'' of thinning and superposition, generalization of Poisson processes. Sections 5.3, 5.4HW10Feb1.pdf
M Feb. 4 Lecture 12: definitions of continuous-time Markov chains, birth and death processes, Chapman-Kolmogorov equation, forward equation, backward equation. Sections 6.2 - 6.4.No Assignment
WFeb. 6 Lecture 13: limiting probabilities, time reversibility. Sections 6.5, 6.6. Reading: Section 6.1-6.6 (may skip Proposition 6.1 and Example 6.8 on p.382)
HW11: Exercise 6.3, 6.5, 6.14, 6.20, 6.23 due Wed Feb. 13.
FFeb. 8 Lecture 14: Definition of renewal processes, renewal function, renewal equation. Sections 7.2. HW12: Exercise 7.4, 7.5, due Mon Feb 18 (because no class on Fri Feb 15, college break)
FFeb. 8Midterm Exam, 4-6pm in Eck133. Coverage: Chapter 4-5
M Feb. 11 Lectures 15: limit theorems, stopping time, Wald's equation, elementary renewal theorem.
Reading: Section 7.3 (Skip Example 7.7)
HW13: Exercise 7.12, 7.17 (See Exercise 7.11 for the definition of a delayed renewal process), due Mon, Feb. 18
Problems for Self-Study (Do Not Turn In): Exercise 7.8 (See solutions on p.758-759)
WFeb. 13 Lecture 16: limit theorems, CLT for renewal processes. Section 7.3No Assignment
FFeb. 15College Break, No Class
M Feb. 18Lecture 17: Renewal Reward Processes, Alternating Renewal Processes.
Reading: Section 7.4 and 7.5.1
HW14: Exercise 7.28, 7.32, 7.33, 7.36, due Mon, Feb. 25
Problems for Self-Study (Do Not Turn In):
Example 7.13, 7.14, 7.15 on p.442-444,
Example 7.25, 7.26 on p.454-457
WFeb. 20 Lecture 18: the inspection paradox (Section 7.7),
queueing models (Section 8.1)
HW15: Exercise 7.41, 7.44 on p.492-493, due Wed, Feb. 27
Reading: Section 7.7 Inspection Paradox (p.460-463)
Problems for Self Study: Exercise 7.42 (Solutions on p.761)
FFeb. 22Lecture 19: Little's formula, cost identity (Section 8.2.1), birth-death queueing models (Section 8.3).HW16Feb22.pdf
M Feb. 25 Lecture 20: PASTA principle (Section 8.2.2)
A Markov chain embedded in M/G/1 (Section 8.5)
WFeb. 27 Lecture 21: A Markov Chain embedded in G/M/1 (Section 8.7),
G/M/k, M/G/k (Section 8.9.3-8.9.4),
Gaussian processes, definition of Brownian motion
FMar. 1Lecture 22: Brownian motion as a limit of random walk, conditional distribution (Section 10.1), hitting times, maximum, reflection principle (Section 10.2)HW19Mar1.pdf
M Mar. 4Lecture 23: Arcsine law, zero set of Brownian motionNo Assignment
WMar. 6 Lecture 24: Wald's identities for Brownian motion HW20Mar6.pdf, due Wed, Mar. 13
FMar. 8Lecture 25: More applications of Wald's identitiesHW21Mar8.pdf, due Fri, Mar. 15
MMar. 11Lecture 26: Quadratic Variation.No Assignment
WMar. 13Lecture 27: Ito's Integral, Ito's FormulaNo Assignment
FMar. 15Reading Period, No Class.
M Mar. 18Final Exam, 10:30-1:30pm, Eck133