STAT25300/STAT31700 WINTER 2014

STAT253/317 Winter 2014
Introduction to Probability Models

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

NameOfficeE-mailOffice Hours
Instructor Yibi HuangEckhart 7yibih@uchicago.edu Mon 5-6pm in Eck 131 or by appointment
CAWei SuEckhart 8weisu@galton.uchicago.eduTue 4-5pm in Eck131
Thur 2-3pm in Eck131 or by appointment

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

Complete Syllabus: Click Here

Announcements

  • (2014/01/31) Midterm Exam Announcement and Study Guide
  • (2014/02/03) Here is a Sample Midterm Exam and the solutions for practice
  • (2014/02/12) Solutions to the Midterm Exam
  • (2014/03/12) Final Exam Announcement and Study Guide
  • (2014/03/14) Office Hours During the Week of the Final Exam
  • (2014/03/21) Solutions to the Final Exam
  • Course Schedule, Handouts, and Assignments

    DateTopics and SlidesAssignments (Solutions are posted on Chalk)
    M Jan. 06Severe weather, class canceled
    W Jan. 08 Lecture 1: Definitions of Markov chains, transition probabilities, Ehrenfest diffusion models, discrete queueing models, Sections 4.1 HW1Jan8.pdf
    FJan. 10 Lecture 2: Chapman-Kolmogorov Equation. Sections 4.2 HW2Jan10.pdf
    MJan. 13 Lecture 3: Classification of states (recurrent, transient), recurrence and transience of simple random walks. Section 4.3, p.204-210 HW3.txt
    W Jan. 15 Lecture 4: Limiting distribution I. Sections 4.4No Assignment
    FJan. 17 Lecture 5: Limiting distribution II. Sections 4.4.HW4Jan17.pdf
    M Jan. 20Martin Luther Kings' Day, No Class
    WJan. 22 Lecture 6: Backward Markov chain, time reversibility, detailed balanced equation. Sections 4.8HW5Jan22.pdf
    FJan. 24 Lecture 7: Trick of one-step conditioning, branching Processes. Sections 4.7.HW6.txt
    MJan. 27 Lecture 8: Generating FunctionsHW7Jan27.pdf
    W Jan. 29 Lecture 9: Exponential distributions, memoryless property, definitions of Poisson processes. Reading: Section 5.1-5.2
    HW8: Exercise 5.20, 5.22, 5.22 on p.357 due Fri Feb. 7
    FJan. 31 Lecture 10: Interarrival times of a Poisson process, conditional distribution of interarrival times. Sections 5.3.HW9.txt
    MFeb. 3 Lecture 11: Thinning, superposition, "converse'' of thinning and superposition, generalization of Poisson processes. Sections 5.3, 5.4HW10.txt
    W Feb. 5 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
    FFeb. 7 Lecture 13: Limiting probabilities, time reversibility. Sections 6.5, 6.6. HW11.txt
    MFeb. 10 Lecture 14: Definition of renewal processes, renewal function, renewal equation. Sections 7.2. HW12.txt
    MFeb. 10Midterm Exam, 6:30-8:30pm in Eck133.
    Read the Midterm Exam Coverage and Study Guide
    Here is a Sample Midterm Exam and its solutions for practice
    (2014/02/12) Solutions to the Midterm Exam
    W Feb. 12 Lectures 15: Limit theorems, stopping time, Wald's equation, elementary renewal theorem.
    Reading: Section 7.3 (Skip Example 7.7)
    HW13.txt
    FFeb. 14College Break, No Class
    MFeb. 17 Lecture 16: limit theorems, CLT for renewal processes. Section 7.3HW14.txt
    W Feb. 19Lecture 17: Renewal Reward Processes, Alternating Renewal Processes.
    Reading: Section 7.4 and 7.5.1
    HW15.txt
    FFeb. 21 Lecture 18: the inspection paradox (Section 7.7),
    queueing models (Section 8.1)
    HW16.txt
    MFeb. 24Lecture 19: Little's formula, cost identity (Section 8.2.1), birth-death queueing models (Section 8.3).HW17Feb24.pdf
    W Feb. 26 Lecture 20: PASTA principle (Section 8.2.2)
    A Markov chain embedded in M/G/1 (Section 8.5)
    HW18Feb26.pdf
    FFeb. 28 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
    HW19Feb28.pdf
    MMar. 3Lecture 22: Brownian motion as a limit of random walk, conditional distribution. Section 10.1No Assignment
    W Mar. 5Lecture 23: Hitting Time, Maximum, Re?ection Principle. Section 10.2HW20Mar5.pdf
    FMar. 7 Lecture 24: Wald's identities for Brownian motion No Assignment
    MMar. 10Lecture 25: More applications of Wald's identitiesHW21Mar10.pdf, due Fri, Mar. 15
    WMar. 12Lecture 26: Quadratic Variation.No Assignment
    FMar. 14Reading Period, No Class.
    W Mar. 19Final Exam, 4-6pm, in Eck133
    Read the Final Exam Coverage and Study Guide
    (2014/03/21) Solutions to the Final Exam