6.041SC | Fall 2013 | Undergraduate

Probabilistic Systems Analysis and Applied Probability

Unit III: Random Processes

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This unit provides an introduction to some simple classes of discrete random processes. This includes the Bernoulli and Poisson processes that are used to model random arrivals and for which we characterize various associated random variables of interest and study several general properties. It also includes Markov chains, which describe dynamical systems that evolve probabilistically over a finite state space. We present the general structure of Markov models and study both their long-term and transient behavior.

Lecture 13: Bernoulli Process

Lecture 14: Poisson Process - I

Lecture 15: Poisson Process - II

Lecture 16: Markov Chains - I

Lecture 17: Markov Chains - II

Lecture 18: Markov Chains - III

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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Lecture Topics

  • Definition of Bernoulli process
  • Random processes, more generally
  • Basic properties of the Bernoulli process
  • Distribution of interarrival times
  • The time of the kth success
  • Merging and splitting

Lecture Activities

Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
 1 Bernoulli Process Practice Qing He

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

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Lecture Topics

  • Review of Bernoulli process
  • Definition of Poisson process
  • PMF of number of arrivals
  • Distribution of interarrival times
  • Other properties of the Poisson process

Lecture Activities

Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
 3 Competing Exponentials Jimmy Li

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

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Lecture Topics

  • Review of Poisson process
  • Merging and splitting
  • Examples
  • Random incidence

Lecture Activities

Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
 3 Random Incidence Under Erlang Arrivals Jimmy Li

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 7 covers Lectures 13, 14, and 15.

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Lecture Topics

  • Checkout counter example
  • Markov process definition
  • n-step transition probabilities
  • Classification of states

Lecture Activities

Recitation Problems and Recitation Help Videos

Review the recitation problems in the PDF file below and try to solve them on your own. Two of the problems have an accompanying video where a teaching assistant solves the same problem.

Recitation Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
1 Setting Up a Markov Chain Jimmy Li
3 Markov Chain Practice 1 Qing He

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

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Lecture Topics

  • Review
  • Steady-state behavior
    • Steady-state convergence theorem
    • Balance equations
  • Birth-death process

Lecture Activities

Tutorial Problems

Review the tutorial problems in the PDF file below and try to solve them on your own.

Problem Set and Solutions

Work the problems on your own and check your answers when you’re done. Problem set 8 covers Lectures 16 and 17.

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Lecture Topics

  • Review of steady-state behavior
  • Probability of blocked phone calls
  • Calculating absorption probabilities
  • Calculating expected time to absorption

Lecture Activities

Recitation Problems

Review the recitation problems in the PDF file below and try to solve them on your own.

Tutorial Problems and Tutorial Help Videos

Review the tutorial problems in the PDF file below and try to solve them on your own. One of the problems has an accompanying video where a teaching assistant solves the same problem.

Tutorial Help Videos

PROBLEM # PROBLEM TITLE PROBLEM SOLVED BY
2 Mean First Passage and Recurrence Times Kuang Xu

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Course Info

As Taught In
Fall 2013
Learning Resource Types
Lecture Videos
Recitation Videos
Problem Sets with Solutions
Exams with Solutions