A study by Forbes indicated that the five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam email are given below. shipping! 0.051 today! 0.045 here! 0.034 available 0.014 fingertips! 0.014 Also suppose that the proportions of ham messages that have these words are: shipping! 0.0015 today! 0.0022 here! 0.0022 available 0.0041 fingertips! 0.0011 a. If a message includes the word shipping!, what is the percent probability the message is spam? If a message includes the word shipping!, what is the percent probability the message is ham? Should messages that include the word shipping! be flagged as spam? b. If a message includes the word today!, what is the percent probability the message is spam? If a message includes the word here!, what is the percent probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? c. If a messages includes the word available, what is the percent probability the message is spam? If a message includes the word fingertips!, what is the percent probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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A study by Forbes indicated that the five most common words appearing in spam emails are
shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email
not considered to be spam) through application of Bayes' theorem. Suppose that for one email
account, 1 in every 10 messages is spam and the proportions of spam messages that have the five
most common words in spam email are given below.
shipping! 0.051
today!
0.045
here!
0.034
available 0.014
fingertips! 0.014
Also suppose that the proportions of ham messages that have these words are:
shipping! 0.0015
today!
0.0022
here!
0.0022
available 0.0041
fingertips! 0.0011
a. If a message includes the word shipping!, what is the percent probability the message is spam?
If a message includes the word shipping!, what is the percent probability the message is ham?
Should messages that include the word shipping! be flagged as spam?
b. If a message includes the word today!, what is the percent probability the message is spam? If a
message includes the word here!, what is the percent probability the message is spam? Which of
these two words is a stronger indicator that a message is spam? Why?
c. If a messages includes the word available, what is the percent probability the message is spam?
If a message includes the word fingertips!, what is the percent probability the message is spam?
Which of these two words is a stronger indicator that a message is spam? Why?
d. What insights to the results of parts (b) and (c) yield about what enables a spam filter that uses
Bayes' theorem to work effectively?
Transcribed Image Text:A study by Forbes indicated that the five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam email are given below. shipping! 0.051 today! 0.045 here! 0.034 available 0.014 fingertips! 0.014 Also suppose that the proportions of ham messages that have these words are: shipping! 0.0015 today! 0.0022 here! 0.0022 available 0.0041 fingertips! 0.0011 a. If a message includes the word shipping!, what is the percent probability the message is spam? If a message includes the word shipping!, what is the percent probability the message is ham? Should messages that include the word shipping! be flagged as spam? b. If a message includes the word today!, what is the percent probability the message is spam? If a message includes the word here!, what is the percent probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? c. If a messages includes the word available, what is the percent probability the message is spam? If a message includes the word fingertips!, what is the percent probability the message is spam? Which of these two words is a stronger indicator that a message is spam? Why? d. What insights to the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?
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