# An Introduction to Artificial Intelligence Week 8

**Course Name: An Introduction to Artificial Intelligence**

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**These are An Introduction to Artificial Intelligence Answers Week 8**

**These are An Introduction to Artificial Intelligence Answers Week 8****For Question 1 to 3 – **

**Q1. Minimum number of values required to store the above Bayes net is**

**Answer: 9**

**Q2. Which of the following are true about the above bayesian network?**

a. C is conditionally independent of D, given A.

b. C is conditionally independent of D, given E.

c. B is conditionally independent of A, given C.

d. B is conditionally independent of C, given A

**Answer: a. C is conditionally independent of D, given A.**

**These are An Introduction to Artificial Intelligence Answers Week 8**

**Q3. Given C and D, E is independent of which of the following variables? (Select only one option)**

a. A

b. B

c. Both A and B

d. Neither A nor B

**Answer: d. Neither A nor B**

**Q4. Which of the following statements are true?**

a. Bayesian network can be used to find the number of satisfying assignments for any Boolean formula

b. Inference in a Bayesian network always has exponential time complexity, irrespective of structure

c. Inference in a Bayesian network may be polynomial time for certain structures of the network

d. Cut sets can simplify inference in Bayesian networks

**Answer: c, d**

**These are An Introduction to Artificial Intelligence Answers Week 8**

**Q5. Which of the following will always hold?**

a. P(a,b) = P(a|b)P(b)

b. P(a,b|c) = P(a|c)P(b|c)

c. 1 = P(a|¬b) + P(a|b)

d. P(a,b|c) = P(b|c)P(a|b,c)

**Answer: a. P(a,b) = P(a|b)P(b)**

**Q6. Consider the following Bayesian network along with the conditional probabilities given below. What is the value of P(C | D,E)? Give the answer as a decimal rounded to 2 decimal places (for example, 0.12 for 0.1234)**

**P(A) = 0.5, P(B) = 0.4, P(C| A,B) = 0.9, P(C| ¬A,B) = 0.5, P(C| A,¬B) = 0.2, P(C| ¬A,¬B) = 0.1, P(D | C) = 0.8, P(D| ¬C) = 0.2, P(E | C) = 0.1, P(E | ¬C) = 0.4.**

**Answer: 0.42**

**These are An Introduction to Artificial Intelligence Answers Week 8**

**Q7. In the above question, which are the evidence and hidden variables for the computation of P(C | D,E)? Return the answer as evidence variables followed by hidden variables separated by a %, where each group is lexicographically sorted (eg. if evidence is C and D and hidden variable is A, return CD%A).**

**Answer: DE%C**

**Q8. Consider the following joint probability matrix. Each row contains a value for x and each column contains a value for y. What is the value of P(y=2|x=2)? Give the answer as a decimal rounded to 2 decimal places (for example, 0.12 for 0.123)**

**Answer: 0.2**

**These are An Introduction to Artificial Intelligence Answers Week 8**

**Q9. You toss a fair coin 3 times. Given that you observed at least one head, what is the probability that you observed at least 2 heads? If the answer is expressed as m/n where m and n are coprime, give the answer as m+n.**

**Answer: 11**

**Q10. Which of the following statements are correct?**

a. There exists a unique Bayesian network for every joint probability distribution.

b. Multiple valid Bayesian networks can be constructed to represent the same joint probability distributions.

c. Two variables in a bayesian network are conditionally independent if and only if they are d-separated.

d. Bayesian network structures are required to be directed acyclic graphs.

**Answer: b, c, d**

**These are An Introduction to Artificial Intelligence Answers Week 8**

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**These are An Introduction to Artificial Intelligence Answers Week 8**

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