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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.
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 …
