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10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 1/10 14/14 Questions Answered Saved at 6:16 PM

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 2/10 Homework 7 (Part 2)

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 3/10 Q1 Decision Networks 4 Points Assume that you want to watch a film that can either be great or pretty bad . You can either watch the film in a theater or at home by renting it. This is controlled by your choice . Consider the following decision network and tables: Compute the following quantities. and stand for expected and maximum expected utility respectively. Q1.1 1 Point 55 Please justify your answer below by writing the appropriate equation(s) with the terms you used to arrive at your answer: (1/2)*1000 + (1/2)*10 = 55 Save Answer Last saved on Oct 31 at 5:28 PM M + m − m A EU MEU EU ( theater ) =

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10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 4/10 Q1.2 1 Point 60 Save Answer Last saved on Oct 31 at 5:29 PM Q1.3 1 Point 60 Save Answer Last saved on Oct 31 at 5:55 PM Q1.4 1 Point rent Save Answer Last saved on Oct 31 at 5:57 PM EU ( rent ) = MEU (∅) = argmax EU ( A ) = A

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 5/10 Q2 7 Points You would like obtain more information about whether the film is good or not. For that, we introduce another variable which designates the "fullness" (how sold-out the tickets are) in the theaters. This variable is affected by another variable which designates possible Covid-19 restrictions. The prior of and the utilities are the same as before. Assuming that both and are binary, consider the following network and tables: We want to figure out the value of revealing the Covid-19 restrictions . Compute the values of the following quantities. F S M F S S

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 6/10 Q2.1 1 Point 55 Please justify your answer below by writing the appropriate equation(s) with the terms you used to arrive at your answer: Save Answer Last saved on Oct 31 at 6:15 PM Q2.2 1 Point 60 Save Answer Last saved on Oct 31 at 6:15 PM Q2.3 1 Point 60 Save Answer Last saved on Oct 31 at 6:15 PM EU ( theater ∣ + s ) = EU ( rent ∣ + s ) = MEU ({+ s }) =

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10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 7/10 Q2.4 1 Point rent Save Answer Last saved on Oct 31 at 6:15 PM Q2.5 1 Point 60 Save Answer Last saved on Oct 31 at 6:15 PM Q2.6 1 Point rent Save Answer Last saved on Oct 31 at 6:16 PM Q2.7 1 Point 0 Save Answer Last saved on Oct 31 at 6:16 PM Optimal action for + s = MEU ({− s }) = Optimal action for − s = V PI ( S ) =

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 8/10 Q3 6 Points Now let's assume that we want to determine the "fullness" of the theaters without using information about the Covid-19 restrictions but using information about the garbage disposal outside the theaters. This new variable is also binary and the new decision network and tables are as follows: We also provide you with the following extra tables that might help you to answer the question. Fill in the following values: F G

10/31/23, 6:21 PM Submit Homework 7 (Part 2) | Gradescope https://www.gradescope.com/courses/572452/assignments/3582896/submissions/new 9/10 Q3.1 2 Points 67.96 Please justify your answer below by providing the equation(s) you used to arrive at this answer: Save Answer Last saved on Oct 31 at 6:16 PM Q3.2 2 Points 51.72 Save Answer Last saved on Oct 31 at 6:16 PM Q3.3 2 Points 1.3 Save Answer Last saved on Oct 31 at 6:16 PM MEU (+ g ) = MEU (− g ) = V PI ( G ) =

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