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CptS 440/540 Artificial Intelligence
Homework 8

1. Recall the full joint probability distribution from HW7 (reproduced below). Suppose we are told that Uniform and Weather are independent of each other, and that Win depends on both Uniform and Weather. Show a Bayesian network consistent with this information. Be sure to show all nodes, links, and conditional probability tables (CPTs). Use the full joint probability distribution below to compute the CPT entries.

Win true fa lse
Uniform crimson gray crimson gray
Weather clear 0.18 0.08 0.06 0.08
cloudy 0.08 0.10 0.07 0.09
rainy 0.05 0.09 0.08 0.04

2. Using the Bayesian network on the next page, compute the following probabilities. Show your work.
a. P(Uniform=crimson, Weather=clear, Win=true, CallFriends=true, BuyJersey=true)
b. P(CallFriends=true | Uniform=gray, Weather=cloudy)
c. P(Uniform=crimson | CallFriends=true, BuyJersey=true)

3. What would be the most likely sample from applying direct sampling to the Bayesian network in Problem 2? What is this sample’s probability?

4. CptS 540 Students Only. In Problem 1 above, we are told that Uniform and Weather are independent of each other. Is that information consistent with the full joint probability distribution? Justify your answer.
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