1. Do the following exercises based on the Bayesian network shown in Figure 14.12a:

   1. Implement the network using the AIMA Python tools.
   2. Compute the number of independent values in the full joint probability distribution for this domain. Assume that no conditional independence relations are known to hold between these values.
   3. Compute the number of independent values in the Bayesian network for this domain. Assume the conditional independence relations implied by the Bayes network.
   4. Compute probabilities for the following:
      1. P(Cloudy)
      2. P(Sprinker | cloudy)
      3. P(Cloudy| the sprinkler is running and it’s not raining)
      4. P(WetGrass | it’s cloudy, the sprinkler is running and it’s raining)
      5. P(Cloudy | the grass is not wet)

      Provide both computer-generated solutions and hand-worked derivations of how these numbers are computed.

Final project suggestion: Consider building an expert system for some knotty problem, comparing and contrasting the traditional, rule-based technologies with the newer Baysian-network-based technologies.

Checking in

Submit the files specified above in Moodle under homework 6. We will grade your work according to the following criteria:

• Exercise 1 - Complete the program as specified above.
  1. 20% - Implement the network properly.
  2. 10% - Compute the appropriate value.
  3. 10% - Compute the appropriate value.
  4. 60% - Compute the values correctly and include hand-executed demonstrations.