EECS 391/491: PROBLEM SET #8

Reading:

Problem 8.1 [10 points]

Problem 19.1 of Nilsson, reprinted below:

Hint: Use Bayes' rule.

Problem 8.2 [15 points]

Problem 19.3 of Nilsson, reprinted below:

Problem 8.3 [15 points]

Problem 19.4 of Nilsson, reprinted below:

Problem 8.4 [15 points]

Problem 19.6 of Nilsson, reprinted below:

Problem 8.5 [15 points]

Define fuzzy sets that can be used to represent the following concepts:
  1. Old (domain is real-valued age in years).
  2. Not old (domain is real-valued age in years).
  3. Young (domain is real-valued age in years).
  4. A few (domain is positive integers).
(e) Do "not old" and "young" have to be the same?

The following two problems require some programming.

Problem 8.6 [15 points]

Check your answer to Problem 8.2 above with a Monte Carlo simulation (using direct or rejection sampling). Turn in your code and a summary of your results.

Problem 8.7 [15 points]

Is a Monte Carlo simulation with direct or rejection sampling practical in verifying the answer to Problem 8.3 above? Why or why not? If not, can you think of any modifications that would make such a simulation practical? Turn in code and a summary of any results in support of the above.

The following problem is for graduate students only.

Problem 8G.1 [20 points]

Problem 14.11 from R&N
Author: Michael S. Branicky.