he five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters eparate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email ccount, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam mail are given below. chipping! oday! mere! available ingertips! 0.049 0.044 0.035 0.012 0.012 Iso suppose that the proportions of ham messages that have these words are chipping! 0.0013 oday! 0.0023 ere! 0.0023 vailable 0.0039 ingertips! 0.0010 ound your answers to three decimal places.
he five most common words appearing in spam emails are shipping!, today!, here!, available, and fingertips!. Many spam filters eparate spam from ham (email not considered to be spam) through application of Bayes' theorem. Suppose that for one email ccount, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam mail are given below. chipping! oday! mere! available ingertips! 0.049 0.044 0.035 0.012 0.012 Iso suppose that the proportions of ham messages that have these words are chipping! 0.0013 oday! 0.0023 ere! 0.0023 vailable 0.0039 ingertips! 0.0010 ound your answers to three decimal places.
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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Transcribed Image Text:**Spam and Ham Words Analysis Using Bayes' Theorem**
In the context of email filtering, it is crucial to distinguish between spam and ham (non-spam) messages. This differentiation process often employs Bayes' theorem, a mathematical formula used for calculating conditional probabilities. Below, we explore the frequency of certain words in spam and ham emails, which aids in identifying spam.
### Common Words in Spam Emails
The five most common words that appear in spam emails are:
- **shipping!**: Appears in 4.9% of spam emails.
- **today!**: Appears in 4.4% of spam emails.
- **here!**: Appears in 3.5% of spam emails.
- **available**: Appears in 1.2% of spam emails.
- **fingertips!**: Appears in 1.2% of spam emails.
### Common Words in Ham Emails
Conversely, the same words appear with lower frequency in ham emails as follows:
- **shipping!**: Appears in 0.13% of ham emails.
- **today!**: Appears in 0.23% of ham emails.
- **here!**: Appears in 0.23% of ham emails.
- **available**: Appears in 0.39% of ham emails.
- **fingertips!**: Appears in 0.10% of ham emails.
### Statistical Context
Consider a scenario where one out of every ten emails is spam. By leveraging the observed probabilities of word occurrences (as listed above) and applying Bayes' theorem, spam filters can enhance accuracy in classifying emails. This method analyses the likelihood ratios of word occurrences in spam versus ham messages.
Using this information, spam filters can calculate the probability that an email is spam given the presence of these words, refining filters for better precision.
**Note**: All values are rounded to three decimal places for precision.
![Certainly! Here’s the transcription of the image for an educational website:
---
**Probability Analysis in Spam Detection**
**a.** If a message includes the word *shipping!*, what is the probability the message is spam?
Probability: **0.80**
If a message includes the word *shipping!*, what is the probability the message is ham?
Probability: **0.19**
Should messages that include the word *shipping!* be flagged as spam?
Decision: **Yes**
---
**b.** If a message includes the word *today!*, what is the probability the message is spam?
Probability: [Text box for input]
If a message includes the word *here!*, what is the probability the message is spam?
Probability: [Text box for input]
Which of these two words is a stronger indicator that a message is spam?
Dropdown: **- Select your answer -**
Why?
Because the probability is
Dropdown: **- Select your answer -**
---
**c.** If a message includes the word *available*, what is the probability the message is spam?
Probability: [Text box for input]
If a message includes the word *fingertips!*, what is the probability the message is spam?
Probability: [Text box for input]
Which of these two words is a stronger indicator that a message is spam?
Dropdown: **- Select your answer -**
Why?
Because the probability is
Dropdown: **- Select your answer -**
---
**d.** What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?
Explain:
[Text box for input]
It is easier to distinguish spam from ham when a word occurs
Dropdown: **- Select your answer -**
in spam and less often in ham.
---
This exercise illustrates the application of probability and Bayes' theorem in evaluating and filtering spam messages based on the occurrence of specific words.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbe4d004-b0c7-4fb9-bd84-121b248ea820%2Fdeb535af-0625-4825-930e-93c34bb38577%2Feautubr_processed.png&w=3840&q=75)
Transcribed Image Text:Certainly! Here’s the transcription of the image for an educational website:
---
**Probability Analysis in Spam Detection**
**a.** If a message includes the word *shipping!*, what is the probability the message is spam?
Probability: **0.80**
If a message includes the word *shipping!*, what is the probability the message is ham?
Probability: **0.19**
Should messages that include the word *shipping!* be flagged as spam?
Decision: **Yes**
---
**b.** If a message includes the word *today!*, what is the probability the message is spam?
Probability: [Text box for input]
If a message includes the word *here!*, what is the probability the message is spam?
Probability: [Text box for input]
Which of these two words is a stronger indicator that a message is spam?
Dropdown: **- Select your answer -**
Why?
Because the probability is
Dropdown: **- Select your answer -**
---
**c.** If a message includes the word *available*, what is the probability the message is spam?
Probability: [Text box for input]
If a message includes the word *fingertips!*, what is the probability the message is spam?
Probability: [Text box for input]
Which of these two words is a stronger indicator that a message is spam?
Dropdown: **- Select your answer -**
Why?
Because the probability is
Dropdown: **- Select your answer -**
---
**d.** What insights do the results of parts (b) and (c) yield about what enables a spam filter that uses Bayes' theorem to work effectively?
Explain:
[Text box for input]
It is easier to distinguish spam from ham when a word occurs
Dropdown: **- Select your answer -**
in spam and less often in ham.
---
This exercise illustrates the application of probability and Bayes' theorem in evaluating and filtering spam messages based on the occurrence of specific words.
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