8) I wish to make a decision on whether or not a storm is likely to occur based on wind speed. Based on an unsupervised learning mechanism, I find that the the observed wind speeds are normally distributed with mean, 4o and variance, of whenever there is no storm and the wind speeds are normal distributed with mean, Hi and variance, of whenever there is a storm. I make n independent observations of the wind speed, X1, X2, ., Xn. Let X = [ X1 X2 X3 ... X ] (" represents transpose). Let 6o represent the truth that there is no storm and 01 represent the truth that there was a storm. a) Write the conditional probability density function, fo(X|0). b) Write the conditional probability density function, fi(X0,). Write the likelihood ratio A(X).
8) I wish to make a decision on whether or not a storm is likely to occur based on wind speed. Based on an unsupervised learning mechanism, I find that the the observed wind speeds are normally distributed with mean, 4o and variance, of whenever there is no storm and the wind speeds are normal distributed with mean, Hi and variance, of whenever there is a storm. I make n independent observations of the wind speed, X1, X2, ., Xn. Let X = [ X1 X2 X3 ... X ] (" represents transpose). Let 6o represent the truth that there is no storm and 01 represent the truth that there was a storm. a) Write the conditional probability density function, fo(X|0). b) Write the conditional probability density function, fi(X0,). Write the likelihood ratio A(X).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![8) I wish to make a decision on whether or not a storm is likely to occur based on wind speed. Based on an
unsupervised learning mechanism, I find that the the observed wind speeds are normally distributed with
mean, µo and variance, of whenever there is no storm and the wind speeds are normal distributed with mean,
ui and variance, of whenever there is a storm. I make n independent observations of the wind speed, X1,
X2, .., Xn. Let X = [ X1 X2 X3 .. X, ]' (" represents transpose). Let 6o represent the truth that
there is no storm and 01 represent the truth that there was a storm.
a)
Write the conditional probability density function, fo(X 60).
b)
Write the conditional probability density function, fi(X|0,).
c)
Write the likelihood ratio A(X).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f189c1d-8acc-4969-8e7a-91f676fd2636%2F312dacc5-b636-4dcf-9cd6-02d408782800%2F2a8dqej_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8) I wish to make a decision on whether or not a storm is likely to occur based on wind speed. Based on an
unsupervised learning mechanism, I find that the the observed wind speeds are normally distributed with
mean, µo and variance, of whenever there is no storm and the wind speeds are normal distributed with mean,
ui and variance, of whenever there is a storm. I make n independent observations of the wind speed, X1,
X2, .., Xn. Let X = [ X1 X2 X3 .. X, ]' (" represents transpose). Let 6o represent the truth that
there is no storm and 01 represent the truth that there was a storm.
a)
Write the conditional probability density function, fo(X 60).
b)
Write the conditional probability density function, fi(X|0,).
c)
Write the likelihood ratio A(X).
Transcribed Image Text:TABLE I
HOURS OF PREPARATION, MID-TERM SCORES AND FINAL EXAMINATION SCORES OF 12 STUDENTS FOR PROBLEM #9).
Hours of
Preparation
(Mid-term) (Percentage) (Final Exam)
Mid-Term
Preparation Performance
Hours of
Final Exam
Performance
(Percentage)
83
12
71
15
08
49
12
62
15
80
14
76
14
73
14
77
22
93
21
89
17
85
13
74
10
58
08
48
16
82
15
78
10
64
12
76
05
32
09
51
20
87
13
73
18
80
21
89
d)
Show that X? is a sufficient statistic for me to make a decision if = 4.
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