Homework Help is Here – Start Your Trial Now!
Math
Statistics
3. a) Prove that E[A"(x)l H,] = E[A®™'(x)| H.]. where El·T:] represents a conditional expectation and A"(x) denotes the likelihood ratio raised (LRT) to the nth power . H, and H, represent hypothesis one or null (samples are from class d, or d.) b) The identity you proved in part (a) can be written equivalently as so, choosing n= 0, we know that PATH,) = Ap(ATH,). We also know that FA where T is the threshold in the LRT.

3. a) Prove that E[A"(x)l H,] = E[A®™'(x)| H.]. where El·T:] represents a conditional expectation and A"(x) denotes the likelihood ratio raised (LRT) to the nth power . H, and H, represent hypothesis one or null (samples are from class d, or d.) b) The identity you proved in part (a) can be written equivalently as so, choosing n= 0, we know that PATH,) = Ap(ATH,). We also know that FA where T is the threshold in the LRT.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
3. a) Prove that E[A^(x)I H.] = E[A™*(x)I H.]. n+1 where E[·I-] represents a conditional expectation and A"(x) denotes the likelihood ratio raised (LRT) to the nth power . H, and H, represent hypothesis one or null (samples are from class d, or d.) b) The identity you proved in part (a) can be written equivalently as n+1 so, choosing n= 0, we know that KATH,) = Ap(ATH,). We also know that Po FA where T is the threshold in the LRT. Given these facts and the fact that T20 (it must be since A(x)2 0) show that: i) the slope of the ROC curve at any operating point (P,, PEA)is just the threshold T required to achieve that point, and ii) the ROC curve is nondecreasing.
Transcribed Image Text:3. a) Prove that E[A^(x)I H.] = E[A™*(x)I H.]. n+1 where E[·I-] represents a conditional expectation and A"(x) denotes the likelihood ratio raised (LRT) to the nth power . H, and H, represent hypothesis one or null (samples are from class d, or d.) b) The identity you proved in part (a) can be written equivalently as n+1 so, choosing n= 0, we know that KATH,) = Ap(ATH,). We also know that Po FA where T is the threshold in the LRT. Given these facts and the fact that T20 (it must be since A(x)2 0) show that: i) the slope of the ROC curve at any operating point (P,, PEA)is just the threshold T required to achieve that point, and ii) the ROC curve is nondecreasing.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS