The final exam is on Tuesday from 8-10. I will have office hours from 8-10 am on Monday.
Here are the solutions to Tuesday's practice sheet.
Here is a link to the solutions to the Charles on Viagra problem and Dicky peeing in the pool problem (which I mislabeled in class.) On Thursday we will review expected value problems and have one last quiz, which will be a couple questions on expected value problems. I will have the exam grades posted by this afternoon or evening.
This week will be all reviewing for final. We will spend Tuesday reviewing the material from the first test and Thursday reviewing the material from the second and since.
Test! You will need a Scantron form 882E (long skinny one) and some number 2 pencils. No calculator. Don't be late. There are 85 questions. You will need the whole period.
We will work through Chapter 12 on IPIL on Tuesday. Thursday is our 3rd test. It is a multiple choice test on TFS covering all but the final two chapters. Here is a link to a .pdf with all the quiz questions to date. It is a large document and will take a while to load. You may need to zoom it a little to be able to read, as I've shrunk the slides down. Most of the questions will be similar to the ones on the slides, some will be identical. However, none of these slides are covering chapters 34-36, and these chapters will be covered on the test. These slides are a better study guide than the ones uploaded on a per quiz basis to einstruction, since I have often marked more than one answer correct on these because a question in its original form was confusing.
For the test you will need a Scantron form 882E (long skinny one) and some number 2 pencils. No calculator.
We will quiz on TFS 31-33 and begin IPIL Chapter 12.
We will cover chapters 10 and 11 in IPIL on Tuesday. Thursday we will have a clicker quiz on TFS 31-33.
Our third test will be a multiple choice test over the entirety of TFS (except for the final two chapters). It will be administered in class on May 3rd. About 3/4 of the questions will be variations on questions I have asked in class for clicker quizzes. These are available on einstruction, but I will also be uploading them to the website as a PDF.
Review chapters 28-30 in TFS and read chapters 10 and 11 IPIL. We'll start with a clicker quiz on the former.
Read Chapter 10, Decision Under Uncertainty. Also, if you want to submit a summary for any Nammour session you attended, be sure to email it to me by Sunday at midnight. Follow the directions carefully in the Attendance credit link in the sidebar.
4/9/12 and 4/11/12
We will not meet on Tuesday because I will be busy with the Nammour Symposium. You can get quiz credit for attending the 10 am session by bringing your clicker. When you arrive, click 'A'. When you leave, click 'A' again. You won't see anything on the screen, but you will see on your clicker whether you answer has been received. To get credit you need to be there for at least the first hour.
You can also get quiz credit by writing summaries per the attendance credit link in the sidebar. Check our syllabus to see the exact rules for this class.
For Thursday we will finish up talking about Maximizing Expected Value in IPIL and we will have a clicker quiz on KFS chapters 28-30.
The lecture 8 link on the schedule page now has all of my notes on expected value. We have our 2nd test on Thursday. By Wednesday morning about half of the test will be posted here. This not a take-home test, you will need to reproduce any answer you work out beforehand in class, and without the assistance of notes. As before, you may use a calculator in class and basic formulas will be provided on the test. Bayes' rule will not be provided, however. The first question of the test will be to derive Bayes' rule using only the definition of conditional probability and the expression of total probability (both of which will be provided.). This derivation is in the book, but the one in the notes is, I think, easier to follow.
Some or all of the following problems will be on the test.
1. Derive Bayes’ Rule for two mutually exclusive and exhaustive hypotheses using the definition of conditional probability and the formula for total probability. Be sure that each step is explicit.
In each of 2, 3 and 4 you will use the value calculated in part a to solve part b.
2a. You are the manager of a big league sports team and your advance Scout Milt is 95% reliable at identifying big league talent in high school players. (This means that 95% of the time Milt says someone will make it in the big leagues he is right; and 95% of the time he says someone won’t make it he is also right.) Big league talent is rare, however. Only about 1 in 10,000 high school players is good enough to play in the bigs. Milt says this kid Tony is a future big leaguer. What’s the probability that he is?
2b. You decide to offer Tony a 2 year contract worth 100,000 dollars. If his not being a major league talent means that Tony will never bring any value to the club, how much value must his turning out to be a future big leaguer represent over this period in order for this to be a fair (i.e. break-even) price? (Note, you are not asked for the value per year, so the length of the contract is not important here.)
3a Alvin has tested positive for an infection that is lethal in 40% of those infected. The virus is extremely rare, but he is in a risk group for which the base rate is .01. The test is 99% reliable for detecting the disease when it is there. It produces false positives at a rate of .02. What is the probability that Alvin has the infection?
3b. Alvin can take a medicine that is guaranteed to kill the virus, but the medicine might also kill him in the process. People who take the medicine survive 80% of the time, which means that they are killed by the medicine 20% of the time. Uninfected people who are given the medicine die only 10% of the time. If Alvin maximizes expected value, will he take the medicine? (Hint: For simplicity, let the utility of survival =1 and death =0.)
4a You are working on an exam and it is getting late. There are two remaining problems and you only have time for one. Problem A is worth 3 pts, Problem B is worth 5 pts. This suggests that A is supposed to be easier than B, but it’s not certain. Also, in this test you actually lose half the value of the question if you get it wrong. Suppose the probability of your solving A is .8 and the probability of solving B is .3. Calculate the expected value of each.
4b. You have some pride and would get more satisfaction out of trying problem B than A. If you measure your satisfaction in terms of points, what is the minimum satisfaction you would require from attempting B in order to make it worth it? (Remember, you will get this satisfaction whether you get B right or wrong. Assume that you will get no negative satisfaction from doing A.)
5a. An elderly lady has stepped out in front of the light rail. She will certainly die if you do not help her, but you can not help her without risking being killed yourself. People of her age and condition have an average of 10 QALY’s remaining. People of your age and condition have an average of 50 QALY’s remaining. If you save her, you will both live without injury. If you fail to save her, you will both die. Using the above figures and taking only your and her QALYs into account, what is the lowest probability of success that will make the expected value of trying to save her worth the risk? (Hint: QALY means “quality adjusted life year.” It is just the amount of value in an average year of human life.)
5b. Suppose that the probability of success is .9 and that you would be racked by guilt for the rest of your life if you failed to help her. How man QALY’s must the value of your life be reduced from not coming to her aid in order to make the expected value of trying to save her worth the risk? (Measure your guilt in terms of QALY’s.)
Work the problems from 3/29 below as well as the following problems. We will do a clicker quiz over these as well as review them in preparation for the test on Thursday.
1. Suppose you are invited to play Rock, Paper Scissors for money. The deal is this. You pay 1 dollar to play. If you tie you get 50 cents back. If you win, you get 3 dollars back. If you lose you get nothing. What is the expected value of this game for you?
2. You are invited to play the following game. I flip a coin. If it lands heads, the game is over and I will pay you a dollar. If it lands tails you get nothing, but I will flip again. This time if it lands heads the game is over and I will pay you 2 dollars. If it lands tails again, I must flip again. This time the payment for heads will be 4 dollars. The game must continue as long as tails keeps coming up. The game must end as soon as heads comes up, and the payment must be exactly double the preceding amount promised for heads. The game continues until the coin lands on heads. What is the expected value of this game for you?
3. There is 1,000 dollars on the table. You and Ralph are to split it with one of you getting 800 and the other getting 200. You are the one who gets to decide. The problem is that if Ralph is dissatisfied he can choose to kill the whole deal, in which case neither of you gets anything. Suppose that Ralph certainly would not kill the deal if you gave him the 800. Ralph might very well kill the deal if he only gets 200 though. What is the minimum probability of this occurring that would make it rational for you to give him the 800? (In this case you and Ralph are never losing any money. You are only gaining 800, 200, or nothing.)
4. The same situation as problem 3. Suppose there is a 90% chance that Ralph will kill the deal if you only give him 200 dollars. How much disutility (in terms of dollars) do you have to experience in contemplation of Ralph getting the larger amount before it is rational for you to give him the smaller amount?
5. You are on the show Let's Make a Deal! There are three different doors and three different prizes: $1,000, $5,000, and $10,000. You choose a door and before it is opened Monty Hall opens another one to reveal 5,000 dollars. He then offers to let you switch. What is the expected value of switching?
Below are three expected value questions similar to those we've been working on in class be sure to solve them because they will be part of the clicker quiz on TFS 25-26.
1. You are planning to study for your test tomorrow but your friends want you to come over and party. You figure there is a 70% chance you will pass even if you don’t study and there is a 90% chance that you will pass if you do study. Suppose partying is worth 5 utiles. Studying is worth 1 utile. (Yes, you actually sort of enjoy studying.) Passing the test is worth 5 utiles and failing it is -5 utiles. Which option, studying or partying, has a greater expected value? What is the exact difference in expected value?
2. You are at your favorite restaurant and trying to decide whether to order your old standby (pizza) or something different (lasagna). The pizza costs 10 dollars and you always get total satisfaction from pizza, which is to say 10 dollars of value. (This makes the expected value of the purchase 0.) The lasagna also costs 10 dollars. If you try the lasagna and are satisfied, you will get bonus pleasure of having tried something new worth 5 dollas, for a total utility of 15 dollars. But if you get the lasagna and you are anything less than satisfied, then you will suffer the extra pain of regret for not having had your old standby so that you would only get 2 dollars worth of value from the lasagna. Question: What is the least probability of satisfaction that would be required to make it worth it to you to try the lasagna?
3. Your dog just got run over and it is going to cost 2,000 dollars to fix him up. Prior to the surgery the dog's life expectancy was 5 more years. If you opt for the surgery it will still be five years, but the quality of life will be 80% of normal. If you don't do the surgery, you will pay 100 dollars to have your dog euthanized and you will feel 400 dollars worth of remorse and guilt. What does the dollar value of a year of your dog's life have to be in order to make the surgery worth the money?
Hope you had a good spring break. For Tuesday and Thursdaay read IPIL Maximizing Expected Value and KFS 25-26. In class on Tuesday we will work more expected value problems. Quiz on KFS on Thursday. Our second test will be Thursday April 5th, covering Bayes' rule and expected value problems.
Today's lecture is posted as Lecture 8 on schedule page. There are a few problems at the end we'll work through on Thursday. You should try them before class. We'll begin with a quiz on TFS 22-24.
Read Chapter 7 Expected Value in IPIL and try problems in back of book. Read chapters 22-24 in TFS. Quiz on the latter on Thursday.
Same assignment as 3/5/12. We will move on to the Expected Value chapter next week.
Continuing with Bayes' Rule and practice problems posted as Lecture 7 from last time. Also, more complex Bayes' rule problems if time permits. Be sure to work all problems from book as well. Quiz Thursday on TFS 19-21.
Continuing with Bayes' Rule and practice problems are posted as Lecture 7. Try the problems, and we'll review them in class.
Read Ch 7 Bayes' Rule in PIL and Chapters 16-18 in TFS. We'll have a quiz on the latter on Thursday.
Test. Closed book. Bring #2 pencils and calculator.
Here are the solutions to CP Practice 2.
Here are the solutions to the practice test. As noted in class, the practice test has more problems than the real test. Also, there will be some problems asking you to explain basic concepts.
Part of today's lecture as well as next Tuesday's lecture on the rules of probability are posted as Lecture 6 on the schedule page. You should study these slides before class on Tuesday.
The test is on Thursday 2/22. It is in class, closed book. You may bring a calculator. Be sure to work the practice problems I posted on 2/16. I won't be talking about them in class, but I will post solutions. Here is a practice test as well. I will post solutions to this on Wednesday. Be sure you have memorized the formulas for addition, multiplication and conditional probability.
Also Tuesday read KFS Ch13-15. We will start with a quiz on those chapters.
I've posted some more conditional probability practice problems on the schedule page CP Practice2. They are more tedious, but good practice for the test next week. Thursday we will quiz on TFS 10-12 and review the Rules of Probability chapter in PIL.
I've posted some extra problem on the schedule page under the link CP Practice. Work these and we'll review as many as we have time for. Read Chapter 5 in PIL and 10-12 in TFS. We'll quiz on the latter Thursday.
We'll be working on examples involving conditional probability. Review the slides from today and check out the associated Khan videos. He explains things a little differently, which you may or may not like. Notice that Khan gives you problems, as well as step-by-step advice for solving them, so you should do as many of those as you need to. It can be a little frustrating at first because the program will tell you that you are wrong if you have rounded off a calculation a little differently, but you will still be able to see if you did it correctly and you can enter the correct solution to move on to the next problem. Also, clicker quiz over chapter 7-9 in TFS.
We will be having our first test on February 23 covering all the material up until that date.
Read chapter 5 on conditional probability in IPIL and Chapters 7-9 in TFS. Quiz on the latter on Thursday.
We will finish Chapter 4 in IPIL and 4-6 in TFS. Check here on Wednesday for quiz questions from the latter . Also, check out Khan supplementary videos on addition and multiplication rules. They're on the schedule page.
1. What are some examples of the priming effect?
2. Is there any way to use your knowledge of priming to inform your own behavior?
3. How does cognitive ease relate to the illusion of remembering and the illusion of truth?
4. According to Kahneman, when you are writing a paper for a class, why is it a bad idea to use unnecessarily big words and complicated syntax?
5. Suppose your job is to write down the bat and ball problem for someone to read, and you will both win 10 dollars if she gets it right. How should you write it?
6. What is the mere exposure effect?
7. What happens to your thinking when you are in a good mood?
Read chapter 4 in IPIL and Chapters 1-4 in TFS. We'll have a quiz on the latter at the beginning of the period. You should work through all of the problems at the end of the IPIL chapters. Hacking answers these problems in the book, so bring questions with ones you don't understand. We will work similar ones in class.
Clicker questions for 1/31
1. What is the difference between the two modes of thinking described by Kahneman?
2. How does the Invisible Gorilla video demonstrate the effects of System 2?
3. What are some of the conflicts between System 1 and System 2?
4. What makes some cognitive tasks more demanding or effortful than others?
5. What is ego depletion and how is it demonstrated?
6. What, according to Kahneman, does the bat and ball example demonstrate?
7. How does Kahneman use the relation between System 1 and System 2 to explain low scores on the Cognitive Reflection Test?
8. What is the priming effect?
Second day of class: 1/26/12
Read Chapters 1-3 of IPIL and 1-3 of TFS. Read the syllabus and register your clicker. Clicker quiz on 1/26 will cover syllabus and basic concepts of logic.
First day of class: 1/24/12
By the first day of class you should have done the following:
1. Get your books and clicker. (see below)
2. Register your clicker online. (see instructions below) and bring it with you the first day of class.
3. Read the syllabus carefully. (see link to syllabus on main page. If it is not there now, it will be shortly.)
These are the course materials you will need to buy or rent.
You can get these at the Hornet bookstore, but feel free to buy them elsewhere, including the Kindle editions of the texts. (Note: If you already own one of the early model e-instruction clickers that looks like this, it will work. But don't buy one now.)
Instructions for registering your clicker.
You will need to go online and register your clicker for this class. Register it according to the instructions on the box or those you were provided with when you purchased or rented it. You will require a credit card. Be careful to register the serial number of your clicker accurately. At some point during the registration process you will be prompted for a class key. This is a unique number associated with the class in which you are enrolling. The class key for this class is:
(Note: the first symbol in the key is the capital letter 'I')
If you do not have a box or instructions for registering your clicker, then do one of the following.
1. If you just acquired this clicker, then click here to register it. You'll need a credit card and the class key above.
2. If you are using a clicker that you have previously registered, click here and log in. Then follow the instructions given in 1 above.
3. A few important points about clickers.