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2. Let say that we know in advance information relating to whether a random incoming email is a spam. Over a certain period, we find that s spam emails arrive and another h emails arrive that are not spam a) Based on the above information, try to estimate p(s), which is the probability that an incoming email is spam, and p(5), which is the probability that an incoming email is not spam. b) Use Bayes' theorem to estimate the probability that an incoming email containing the certain word b is spam, where p(b) is the probability that b appears in a spam email, and g(b) is the opposite of p(b).

2. Let say that we know in advance information relating to whether a random incoming email is a spam. Over a certain period, we find that s spam emails arrive and another h emails arrive that are not spam a) Based on the above information, try to estimate p(s), which is the probability that an incoming email is spam, and p(5), which is the probability that an incoming email is not spam. b) Use Bayes' theorem to estimate the probability that an incoming email containing the certain word b is spam, where p(b) is the probability that b appears in a spam email, and g(b) is the opposite of p(b).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. Let say that we know in advance information relating to whether a random incoming email is a spam. Over a certain period, we find that s spam emails arrive and another h emails arrive that are not spam a) Based on the above information, try to estimate p(s), which is the probability that an incoming email is spam, and p(5), which is the probability that an incoming email is not spam. b) Use Bayes' theorem to estimate the probability that an incoming email containing the certain word b is spam, where p(b) is the probability that b appears in a spam email, and q(b) is the opposite of p(b).
Transcribed Image Text:2. Let say that we know in advance information relating to whether a random incoming email is a spam. Over a certain period, we find that s spam emails arrive and another h emails arrive that are not spam a) Based on the above information, try to estimate p(s), which is the probability that an incoming email is spam, and p(5), which is the probability that an incoming email is not spam. b) Use Bayes' theorem to estimate the probability that an incoming email containing the certain word b is spam, where p(b) is the probability that b appears in a spam email, and q(b) is the opposite of p(b).
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