Please log in to your Saclink account and find the email containing the link to the course evaluation form and the following assessment survey. Extra points for everyone if almost everyone does it. See syllabus for details.
1. Test 3, Tuesday 10:15. Usual rules apply. Bring your usual supplies (calculator, pencils) as well as a Scantron 882E (long skinny one.)
2. Here is a link to the TFS questions asked this semester. (Note: Jenna caught a couple of wrong answers on an earlier version of the slides. (The first one was the Doctor A, Doctor B slide. The second concerned what was better at predicting academic success, a simple predictive rule or a counselor with full access to the student's history. These have been corrected on the current version.)
3. There are still several people who have not done the course evaluation (see green text above.) You are preventing yourself and your fellow classmates from getting needed points! Sarah knows where you live.
4. All of the probability and expected value problems for Test 3 will be based on the following simplified characterization of the game of tennis.
In the game of tennis, one player serves the ball and the other player receives. If the server successfully serves the ball into the service area, then the players play the ball until someone wins the point. On any given point, if the server’s first serve misses the service area, s/he is allowed to serve again. (This is the only way she is allowed to have a second serve.) If the second serve misses as well, this is called a ‘double fault.’ If a double fault occurs, the opponent wins the point and the server begins the next point. Usually a good tennis player’s first serve (call this the A serve) is a more aggressive serve than the second serve (call this the B serve); The A serve is more difficult to return, but it is also less likely than the B serve to land in the service area.
For all of the questions, ignore the fact that the game could end on a particular point. Use I and O to designate a serve being in or out. Use W and L to indicate winning and losing a point. Use AI, AO, BI, BO to indicate the A and B serves landing in and out.
Christie’s A serve lands in the service area 50% of the time. Her B serve lands in the service area 80% of the time. She normally hits her A serve first and her B serve second. However, if she has double faulted on the previous point, then on the next point she will start with her B serve and, if it misses, hit her B serve again.
Here is the first question on the test.
1. Draw the tree representing the information given directly above for two complete points played on Christie's serve, beginning with the A serve.
Be sure to take the time to work this out before class, as drawing it requires some thought and the rest of the questions will depend on having done this correctly . Pay particular attention to the fact that what serve Christie hits, and therefore the correct probabilities, depend on what has happened on the previous point, e.g., once a serve goes in, the next serve will be for the next point.)
Chapter 38 and concluding chapter of TFS. Chapter 13 and 14 IPIL.
Chapters 36 and 37 TFS. Still chapters 11 and 12 IPIL.
I have posted last semester's Test 3 and a solution to the bottom of the schedule page. A few of the questions will be familiar, but most are new and will be good practice.
Review chapter 34 and read chapter 35 TFS. Still on chapters 11 and 12 IPIL, theories of probability.
Chapters 33 and 34 TFS and Chapters 11 and 12 IPIL.
Chapter 10 IPIL and chapter 32 TFS.
Chapter 9 IPIL and Chapters 30 and 31 TFS. Also, review Allais Paradox from Chapter 29 TFS.
Test on Thursday. Test is closed book. Bring a calculator or borrow one from me, but you may not use the calculator on your phone, tablet or computer. Check back here by Wednesday evening because one of the test problems will be posted.
Chapter 8 slides have been updated.
This problem will be on the test. You should solve it beforehand, however you will have to reproduce it without notes.
There are 2 coins in a bag. One is a fair coin. The other has a 90% bias toward heads. You have a choice between two coin flipping games in which you will flip some coin twice. Both of these games cost 3 dollars to play. The payoff for each of these games is as follows.
TT = $6; HH = $4; TH = $1; HT = $1
Game 1: You choose a coin randomly and flip it twice in a row.
Game 2: You choose a coin randomly and flip it. You replace the coin in the bag. You choose a coin randomly again and flip it.
Calculate the expected value of each game.
Read chapter 29 TFS. No new work in IPIL, but finish problems below and review the ones we have done, which are posted to the schedule pale. Also, be sure you can do am explicit step-by-step derivation of Bayes' Rule. This is given to you in the Chapter 7 slides.
There is no class on Tuesday.
Note: Go to the home page for instructions on how to get credit for attending the Nammour Symposium April 16th and 17th. You will need to register your clicker for a Nammour Symposium class. It will not cost you anything.
For Thursday 4.18 read TFS 27 and 28 and IPIL Chapter 9. Work any problems below that you have not already, as well as the following ones.
1. 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 dollars, 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?
2. You’ve decided to rent a classic black and white movie on Amazon. You have narrowed it down to two choices. Citizen Kane and The Maltese Falcon, neither of which you have seen. CK costs 5 dollars and the personalized rating system says that there is an 80% chance that you will like it. MF costs 3 dollars and the rating system says that there is a 60% chance that you will like it. Assuming that the rating system is accurate, and liking the movie means that it was a fair price and disliking it means you got no value, what is the expected value in dollars of each of these purchases? (CK, MF)
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 the rest of the dog's life have to be in order to make the surgery worth the money?
4. You mow the lawn for the old lady who lives next door. Theoretically she pays you 50 dollars each time you do it, which in your view is 10 dollars more than the fair price. But in reality she completely forgets to pay you about 25% of the time and you just never have the heart to tell her when she does. Over the long run are you getting overpaid or underpaid, and by how much?
Read TFS 26 and finish the problems under 4.9.13. Here are a few more to work on as well.
1. Mel is in reasonably good shape for an 85 year old, but he has no savings and his wife Mildred will not get his pension when he dies. For a man of Mel's condition and age, there is a 10% chance he will die in any given year. For a little peace of mind, Mel would like to buy a 200,000 dollar policy to cover the next 5 years of his life. If you were willing to sell Mel a policy at a fair price to cover this period, what would you have to charge him?
2. Manny and Gwen are playing cornhole again at the county fair. Manny has a hit rate of .6 and Gwen has a hit rate of .9. 1 ticket costs a dollar and gives you three beanbags to toss. If you get 1 bag in the hole you get 50 cents. If you get 2 bags in the hole you get $1.50 and if you get 3 bags in the hole you get $3. What is the expected value of Manny's game and what is the expected value of Gwen's game?
3. I am willing to bet 10 dollars against your 5 dollars that Manny or Gwen will get all three beanbags in the hole. (In other words, if I am right, you pay me 5. If I am wrong, I pay you 10.) What is the expected value of this bet to you?
Read TFS 24 and 25 and work the following problems, which will be on the quiz.
1. Suppose you want to buy a 1 million dollar life insurance policy for a flat rate to cover the next 20 years of your life. What would be a fair price if the risk of your dying at anytime during this period is .01? Remember, the expected value of a fair price is 0. (The actual number of years of the policy doesn't figure into this calculation.)
2. Suppose you are on a trip and you want to buy a 6 million dollar accidental death policy, which is what you would say your life is worth to your beneficiaries in financial terms. If the chance that you will die on this trip is 1 in 100,000, and the policy costs 20 dollars, is the expected value (in financial terms alone) of buying the policy higher or lower than the expected value of not buying it?
3. 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?
4. You can play this game for one dollar: Roll a die. If an odd number comes up, you are finished and you have lost your dollar. If an even number comes up you get the value of that number in dollars. What is the expected value of this game?
5. 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 enjoy studying somewhat.) Passing the test is worth 5 utiles and failing it is -5 utiles.
What is the expected utility of partying ?
What is the expected utility of studying?
6. You just bought a new laptop for 1500 dollars and you are trying to decide whether to buy the insurance, which costs 150 dollars and covers you for two years. The insurance covers any breakage. Let’s assume there is a 10% chance that your computer will break during this time, and the average cost of repair is 400 dollars. Is the expected value of buying the policy higher or lower than the expected value of not buying the policy? By how much?
Read TFS 23 and work solved problems and end of Chapter 8. We will work basic expected value problems for most of the period.
Read Chapter 8 IPIL, Expected Value and do problems at the end. Read TFS 21 and 22. Also, I have posted the lecture slides for Chapters 6 and 7 on the schedule page, which include the Bayesian problems we solved in class, as well as a few others. Be sure to review all of these. Also, become practiced at deriving Bayes' Rule from the definition of conditional probability. You will need to do this from memory for the next test.
Read TFS 19 and 20. We will quiz on those chapters and the problems below from 3.19.13.
Read TFS 17 and 18. Work the following problems. Quiz on both.
1. It is Monday morning and you are lying in bed trying to decide whether to get up.Your roommate always leaves for school before you wake up, and you don’t want to get out of bed this early unless the coffee has been made. Your roommate makes a pot of coffee (and leaves enough for you) about 25% of the time. (Assume that when she makes it, there is always enough left for you. Nobody else makes coffee.)
80% of the time when she makes coffee you can smell it from your bed. But 20% of the time you can’t. 70% of the time when she doesn’t make coffee, you don’t smell it. But 30% of the time you have an olfactory hallucination and smell it when it’s not there.
What’s the probability that the coffee has not been made, given that you smell it?
2. Frank arranged to study with his friend Ray for a logic exam. Frank's not a great student, but studying with Ray boosts his chance of passing from 50% to 90%. Unfortunately, Ray is not reliable, and will just flake and not even show up to study about 25% of the time. It turns out Frank passed the test. What's the probability that he studied with Ray?
3. Your neighbor Fred has just been arrested because his fingerprints match those found on a weapon that was used in a murder in another part of town. Fred claims to have been alone at home the night of the murder, but there is no one who can vouch for his whereabouts. Nothing besides the fingerprints tie Fred to the victim, the weapon or the scene of the crime.
Fred’s fingerprints were the only match in a database of 10,000 people all deemed equally likely to have been involved in the crime. With fingerprints, the probability of a false positive is .01. The probability of a false negative is .07.
What is the probability that those are Fred's fingerprints on the gun?
Note: "False positive" in this case means that the test says that these are Fred's prints, but they actually aren't. "False negative" in this case means that the test says they are not Fred's prints, but they actually are. In statistics, a false positive is called a Type 1 error and a false negative is called a Type 2 error.
4. You have just tested positive for a rare disease called Uh-oh. By rare, we mean that it occurs in 1/10,000 people. In other words, for any randomly selected individual, the likelihood that he or she will have Uh-oh is .0001 The test is 99% effective. This means:
99% of the people who have Uh-oh test positive for Uh-oh.
99% of the people who don’t have Uh-oh, test negative for Uh-oh.
What is the probability that you have Uh-oh, given that you have tested positive? Pr(U/P)
5. You have tested positive for the rare disease called Uh-oh described above. Your doctor said that the probability is not high that you have it given just one test, so she orders it again, but again it comes back positive. Now what is the probability that you have Uh-oh?
Read Chapters 15 and 16 TFS. We will cover the derivation of Bayes' Rule and do some Bayes' rule type problems. Be sure to review the solution to the test.
Read chapter 7 IPIL and Chapters 13 and 14 TFS. Quiz covering both.
Test 1 solution has been posted to the bottom of the schedule page. Grades have been posted to e-instruction and exams will be returned on Tuesday. Grades on e-instruction reflect an 8 point curve, which is why some grades are in excess of 50 points.
Test on Thursday. You will need pencils and a calculator. You may not use the calculator on your phone, tablet or computer. I will have extra calculators for those without one. The test is closed book, but I will give you a sheet with relevant equations. I have uploaded the slides on conditional probability and a practice test with a solution. The test you take will have problems similar to the ones on the practice test.
Work the following problems before coming to class. They will be on the quiz, and we will review them, but I won't give you as much time as usual to answer them.
Urn1 Red = .8, Green = .2
Urn 2 Red = .4, Green = .6
1. Two urns are filled with red and green M&M’s in the above proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first draw you get a red one. What is the probability that you will get a green one on the second draw?
2. Two urns are filled with red and green M&M’s in the above proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first draw you get a red one. On the second you get a green one. What is the probability that they came from Urn 2?
3. A single urn has 9 fair coins and 1 two-headed coin. Someone reaches into the urn, randomly pulls out a coin, and begins flipping it. Question: How many heads in a row are needed before you can be 90% sure that it is the two-headed coin?
4. You are about 80% sure that your nephew Dicky just peed in the pool. Dicky will always deny his own wrongdoing, so you ask his brother Ryan, who had a clear view, but who is also a jerk. When Dicky hasn’t done anything bad, Ryan will still blame Dicky about 25% of the time. When Dicky has done something bad, he Ryan will cover up for him about 10% of the time. What is the probability that Dicky peed in the pool given that Ryan says he didn’t?
5. Manny and Gwen just bought a ticket to play cornhole at the carnival, a game in which you throw beanbags through a hole in a piece of plywood. Manny and Gwen each get three beanbags. If either Manny or Gwen gets all 3 beanbags through the cornhole, they win the stuffed barracuda Gwen is one of the best cornhole players in the county with a hit rate of .9. Manny's hit rate is only .6. What is the probability that they get the barracuda?
6. Manny and Gwen came home with the barracuda! What is the probability that Gwen is not the one who won it?
Read TFS Ch 12 and IPIL Chapter 6. We will work conditional proof problems for the majority of the period.
Read TFS Ch 10 and 11. I have re-posted Chapter 4 notes with all problems we have worked in class. Be sure you can do all of these problems on your own. We will review concept of conditional probability and work conditional probability problems on 2.26.
Our first test is set for Tuesday March 5th.
Work through problems from chapter 5 IPIL. Review Chapter 8 TFS and read chapter 9.
Read IPIL Chapter 5 and TFS Chapters 7 and 8. Notes to chapter 4 are on the schedule page.
Be sure you understand all worked problems and exercises in Chapter 4 IPIL. Read Chapter 6 TFS.
Finish reading Chapter 4 IPIL if you haven't already and review Chapter 4 exercises. Read Chapters 4-5 TFS.
Work problems at the end of Chapter 3 (Answers are in back of book). Read Chapter 4 of IPIL and review Chapter 3 of TFS.
Read Chapter 3 IPIL The Gambler's Fallacy and Chapters 1-3 in TFS. Class begins with clicker quiz on both readings.
Hi, for Thursday make sure you've done everything below. Also, read the first two chapters of IPIL. Your quiz will be on the syllabus but it will also involve a few basic questions about logical concepts from these chapters. Remember, your clicker will not work in class unless you've registered it online for this class according to the instructions below. The registration process takes some time, so don't plan on doing this right before class.
Hi and stuff
Hey everyone, this What's Up page is the one you will check regularly to find out about your daily assignments. Please read every bit of what follows, super carefully and do what it says to do.
For Tuesday 1.29 you should
For Thursday 1.31 you need to have done the following:
1. Get all your course materials, which consists of two texts and a clicker (see below).
2. Register your clicker online (see instructions below) and bring it with you the first day of class. We will have our first quiz, which covers the content of the syllabus.
3. Re-read the syllabus carefully (see link to syllabus on main page).
These are the course materials you will need to buy or rent.
You can get these all at the Hornet bookstore. It is fine to buy 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 otherwise get the one offered at the bookstore. There are several different kinds of clickers being used on campus, so be sure to get the one made by e-instruction.)
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:
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.