Description

CptS 440/540 Artificial Intelligence
Homework 7

1. Consider the following full joint probability distribution to help us determine when the Cougars will win. Compute the following probabilities. Show your work.

Win true false
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

a. P(Win=true, Uniform=crimson, Weather=clear)?
b. P(Weather=clear)?
c. P(Uniform=crimson)?
d. P(Win=true | Weather=clear)?
e. P(Win=true | Weather=cloudy Ú Weather=rainy)?

2. Consider the problem with three Boolean random variables: Win, Practice, Healthy. Assume you know only the following information:
• P(Win=true) = 0.7
• P(Practice=true Ù Healthy=true | Win=true) = 0.8
• P(Practice=true Ù Healthy=true | Win=false) = 0.4
Using Bayes rule and normalization, compute P(Win | Practice=true Ù Healthy=true). Note the “P” is boldfaced, so we want a distribution.

a. Define the sets: breeze, known, frontier and other.
b. Following the method in the textbook and lecture, compute the probability distribution P(Pit2,2 | breeze, known). Show your work.

4. CptS 540 Students Only. Suppose an oracle tells the agent in Question 3 that there is a breeze in (3,3). Will this change the probability of a pit in (2,2)? Justify your answer.

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