ME290M, Spring 1999

ME290M
Expert Systems in Mechanical Engineering
Spring 1999, T-Th 12:30-2:00 pm
1165 Etcheverry Hall, Course Control No. 56369 http://best.me.berkeley.edu/~aagogino/me290m/s99

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Discrete Random Events

3/11/99

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Table of Contents

Discrete Random Events

Example: Venn Diagram and Independence

Disk Drive Failure Example

Outcome Sample Spaces

Talus Bone Example

Talus Bone Events

Sample Space for Joint Events

Example: Find probability of E4 = the event that the sum of the two numbers is four.

Example: F᝺ = the event that the product of the two numbers is less than ten

What if the Talus Bones are Biased?

Biased Talus Bones - Probability Mass Function?

Biased Talus Bones - Joint Probabilities

Conditional Probability Expansions of Talus Bone Example

Influence Diagrams & Talus Bone Example: E4

Influence Diagrams & F᝺ Example:

How do we represent both events E and F in the same influence diagram?

E and F are said to be conditionally independent of each other given Di and Sj

Are E and F independent if we do not conditional information on D and S?

Probability Tree Representation

Expectation of a Random Variable

Expectation of a Function of a Random Variable

Probability Mass Function, Pr(x)

Cumulative Probability Distribution, Pr(xŠy|y)

Cumulative Probability is Summation (Integral) of the Mass Function

Complementary Probability Distribution, Pr(x>y|y)

Joint Discrete Mass Functions

Bayesian Pair of Bolts

Bayesian Pair of Bolts: Bayes Theorem

Bayesian Pair of Bolts: Define Events

Author: Alice Agogino

Email: aagogino@newton.me.berkeley.edu

Home Page: http://best.me.berkeley.edu/~aagogino/me290m/s99

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Last updated: 11 March 99
Send Comments to: Alice Agogino, aagogino@me.berkeley.edu
Copyright © 1999 Alice Agogino; All Rights Reserved.