Homework 2 - Chapters 2 and 3

Answer the following questions. Unless otherwise labeled, each question is worth 2 points.

1. Give an example of two rules that have shared facts that would cause a conflict. List methods one could use to resolve the conflict.
2. 2.12: List advantages of rule-based expert systems. What are their disadvantages?
3. 3.1: What is uncertainty? When can knowledge be inexact and data incomplete or inconsistent? Give an example of inexact knowledge.
4. (4 points) Consider the following situation for a spam detector. The probability of an email being spam is 0.55. The probability of the detector labeling an email as spam if the email is a spam is 0.95. The probability of the detector labeling an email as spam when it is not spam is 0.02. Use Bayes rule to determine the probability than the email you just received is spam given that the detector has labeled it as spam.
5. (4 points) A second spam detector is added to the above system. The probability of the second detector labeling an email as spam when it is spam is 0.97. The probability of the second detector labeling an email as spam when it is not spam is 0.05. You have two hypotheses:
   • H1: The email is spam.
   • H2: The email is not spam.
   Let E1 be that the detector in the previous question labels the email as spam. Let E2 be that the second detector labels the email as spam. Calculate P(H1|E1E2) and P(H2|E1E2).
6. 3.5: What are the likelihood of sufficiency and likelihood of necessity? How does an expert determine values for LS and LN?
7. 3.8: Why may conditional probabilities be inconsistent with the prior probabilities provided by the expert? Give an example of such an inconsistency.
8. 3.9: Why is certainty factors theory considered as a practical alternative to Bayesian reasoning? What are the measure of belief and the measure of disbelief? Define a certainity factor.