Introduction to Electrical Engineering and Computer Science I

Discrete Probability

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Session Overview

We’ve been talking about how to analyze and design systems, but we haven’t talked about how to make systems robust under uncertainty. In fact, we haven’t even talked about how to model uncertainty. In this unit, we’ll address the problem that systems we design may have to operate under uncertainty, and that we may want those systems to be able to search the world for possible solutions to problems. We’ll introduce the basics of probability and search in this session, and apply those concepts to our design challenges. The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand (theory) and be able to do (practice) after completing this session, and additional resources. Session 10 Handout: Discrete Probability (PDF)

Session Content

Readings

Read sections 7.1-7.4 of the course notes.

• Chapter 7: Probabilistic State Estimation (PDF)

Lecture Video

Watch the lecture video. The handout and slides present the same material, but the slides include answers to the in-class questions.

• Lecture 10: Discrete Probability and State Estimation

About this Video

Introduction to probability theory, with the goals of making precise statements about uncertain situations and drawing reliable inferences from unreliable observations. A hidden Markov model is then applied to robot navigation.

• Lecture handout (PDF)
• Lecture slides (PDF)

Recitation Video

These videos have been developed for OCW Scholar, and are designed to supplement the lecture videos.

• Recitation 13: Probability: Basics

Session Activities

The problems in the tables below are taken from the 6.01 Online Tutor, an interactive environment that is not available on OCW. Do not try to answer these questions in the PDF files; answers will not be checked, and cannot be submitted.

Software Lab

• Software Lab 10: Distributions (PDF)
• Code for Software Lab 10 (ZIP) (This ZIP file contains: 1 .py file.)

PROBLEM #	QUESTIONS
10.1.1	Probability distributions: DDist (PDF)
10.1.2	Conditional distributions (PDF)
10.1.3	Joint distributions (PDF)
10.1.4	Operations on conditional distributions (PDF)
10.1.5	Where are you? (PDF)
10.1.6	Implementing joint distributions (PDF)
10.1.7	Implementing operations on conditional distributions (PDF)

Design Lab

• Design Lab 10: Robot Pets (PDF)
• Code for Design Lab 10 (ZIP) (This resource contains: 1 .py file and 1 .pyc file.)

Additional Exercises

PROBLEM #	QUESTIONS
10.3.1	A distribution (PDF)
10.3.2	Summing to 1 (PDF)
10.3.3	Truth (PDF)
10.3.4	Equivalence (PDF)
10.3.5	Buying a car (PDF)

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