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.

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

### 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

### 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

### 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

### 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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### 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

### 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

Fall 2013
##### Learning Resource Types
Lecture Videos
Recitation Videos
Problem Sets with Solutions
Exams with Solutions