Lecture 29: Conditional Distributions & Decision Making in Probability - Univ. of Illinois, Study notes of Statistics

A set of lecture slides from the university of illinois at urbana-champaign's electrical and computer engineering department for ece 313 - probability with engineering applications, fall 2000. The slides cover the topics of conditional distributions, decision making, and the maximum likelihood rule with examples. The slides also discuss the application of these concepts to a radar system.

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Pre 2010

Uploaded on 03/16/2009

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ECE 313 — Probability with Engineering Applications Fall 2000
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign 28.1
Lecture 29 - Conditional Distributions
Professor Seth Hutchison
for Dilip V. Sarwate
Department of Electrical and
Computer Engineering
© 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign. All Rights Reserved
ECE 313
Probability with Engineering Applications
ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 1 of 11
Conditional Distributions
ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 2 of 11
Conditional Distributions, cont.
ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 3 of 11
Decision Making
ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 4 of 11
Plan B
ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 5 of 11
Maximum Likelihood Rule for…
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Download Lecture 29: Conditional Distributions & Decision Making in Probability - Univ. of Illinois and more Study notes Statistics in PDF only on Docsity!

ECE 313 — Probability with Engineering Applications Fall 2000

Department of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign 28.

Lecture 29 - Conditional Distributions

Professor Seth Hutchison

for Dilip V. Sarwate

Department of Electrical and

Computer Engineering

© 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign. All Rights Reserved

ECE 313

Probability with Engineering Applications

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 1 of 11

Conditional Distributions

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 2 of 11

Conditional Distributions, cont.

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 3 of 11

Decision Making

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 4 of 11

Plan B

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 5 of 11

Maximum Likelihood Rule for…

ECE 313 — Probability with Engineering Applications Fall 2000

Department of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign 28.

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 6 of 11

Example: Radar System

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 7 of 11

In General

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 8 of 11

In General, cont.

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 9 of 11

Suppose we pick threshold θ

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 10 of 11

Bayes Decision Rule

ECE 313 - Lecture 29 © 2000 Seth Hutchinson, University of Illinois at Urbana-Champaign, All Rights Reserved Slide 11 of 11

How to choose θ …