CSE 311A: Introduction to Intelligent Agents Using Science Fiction Spring 2020

Homework 2

Due: 11:59pm, February 9, 2020 (on Canvas)

Provide your answers to the following questions in a PDF ﬁle and upload it to Canvas by the deadline.

Question 1 [30 points]

Read the short story “Runaround” by Isaac Asimov. You can access it (as well as other short stories in the “I, Robot” collection) through this link: https://web.williams.edu/Mathematics/sjmiller/public_html/ 105Sp10/handouts/Runaround.html

1a) Describe, in your own words, why Speedy was circling the selenium pool and how it was able to break the loop. 1b) Model Dr. Powell’s decision-making process using a decision tree. En- sure that your tree accurately captures Speedy’s actions as well. 1c) What is the best action or best sequence of actions for Dr. Powell to take according to your tree. Explain how you capture Speedy’s actions within your decision tree.

1 Question 2 [30 points]

This is a modiﬁed scenario from Interstellar. The crew of Endurance can visit two planets (Mann’s and Edmunds’). They can choose to visit neither planets, one of the two planets, or both planets. The characteristics of Mann’s planet are below:

• 30% chance of ﬁnding a perfectly habitable planet

• can support all of Earth’s current population if it is

• can support none of Earth’s population if it is not

And the characteristics of Edmunds’ planet are below:

• 50% chance of ﬁnding a perfectly habitable planet

• can support 50% of Earth’s current population if it is (because it is not as large as Mann’s planet)

• can support 20% of Earth’s current population if it is not (because it is still partially habitable)

The crew also needs to decide when to send a message to Earth to let them know which planet to migrate to. The possible outcomes for the diﬀerent time steps of when they send that message are below:

• If they send the message before visiting both planets, none of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting only one planet (either one), 10% of the Earth’s population would have perished on Earth before receiving that message.

• If they send the message after visiting both planets, 25% of the Earth’s population would have perished on Earth before receiving that message.

2 What should the crew do to save as many of Earth’s population as possible? Speciﬁcally, which planet or planets should they visit, if any and in what order, and when should they send the message to Earth? Draw a decision tree to solve this problem.

Question 3 [40 points]

Imagine a lottery system, where a non-recurring-4-digit number will be chosen at random, i.e., it is not possible for a number with 2 identical digits to be chosen. You can buy up to 5 lottery tickets, where each ticket is associ- ated with a diﬀerent 4-digit number of your choice. If you bought a ticket with the winning number, then you win $5000. Each lottery ticket costs $1. Assume that you can buy up to 5 lottery tickets because you only have $5.

3a) Assume that you only bought 1 lottery ticket. What is the probability that this ticket has the winning number?

3b) Assume that you are risk-neutral. How many lottery tickets would you buy? Justify your decision using a decision tree for this problem.

3c) Assume that you know the second digit of the winning number is 8 with complete certainty and you bought 1 lottery ticket with 8 as the second digit. What is the probability that this ticket has the winning number?

3d) Assume that you are risk-neutral. Additionally, assume that someone oﬀers to sell you the identity of the second digit of the winning number for $4000. Would you buy that information? Justify your decision using a decision tree for this problem.