The final exam is on Tuesday 12/13 from 12-45 to 2:45 PM. You may use a calculator. It is closed book, but I will provide on the exam the basic rules for calculating probabilities and expected values. (This is instead of everyone bringing their own piece of paper, which I said you can do in class.)
We will be covering chapters 13-15 during the last class meetings, approximately 1 chapter per class. Test 5 will be given in class on the date of the final, which is Tuesday December 13th at 12:45. This test is comprehensive. There are two options for how this test may be counted.
Option 1: Single counted as 1 20 pt. test
Option 2: Double counted as 2 20 pt. tests
In Option 2, one of the grades will be substituted for your lowest previous grade. You do not need to select between these two options. I will maximize your value.
For those who took the test home, it has been posted to the schedule page in both PDF and Word format. You may turn in an untyped test, but take-home standards of neatness apply' i.e., no scratchouts, hard to read or disorganized anything. Test is due Tuesday at the beginning of class. 10% off for being turned in after class and no test accepted after Tuesday afternoon office hours.
Chapters 11 & 12 on Tuesday.
Test will be entirely in-class. I have uploaded the lecture slides covering chapters 8,9 and 10 to the bottom of the schedule page (but see correction notice above.) Be sure you can work all the solved problems in the book and all the problems in the slides and that you can still determine conditional probabilities, as at least one question will require you to do this, perhaps more.The test is closed book. E-mail me with questions. You MAY use calculator's this time and you may have one sheet with equations on it. (Axioms of probability, Bayes' rules, expected value.)
Homework note: The answer to problem 2 on p. 111 may appear to some of you to be a mistake. Hacking asks you to determine the value of the inconvenience you attach to losing the old bicycle (over and above the replacement cost.) He says it is (more than) 40 dollars, but it might appear to you that it should be 4 dollars, because this is the difference in the expected value of the kryptonite lock and the cheap lock in problem 1. However, the difference between the two expected values does not tell you the negative value of losing the old bike. To compute this value you would set the expected value equation for the cheap lock equal to -20 dollars (which is the expected value of the kryptonite lock) and put in (-x) for the negative value of losing the bike. So, the expected value equation would be:
.10(-8-80-x) + .90(-8) = -20
If you solve this equation x will come out to equal -40 dollars. Be sure you understand this!
Finishing chapter 10 and beginning Chapter 11 on the meaning of probability claims. The test on 8, 9 and 10 will be Tuesday 10/22. It will be entirely in class and will consist of decision problems like the ones we have been discussing. I will be posting the slides from these 3 chapters on line as a study guide. Be sure you have not forgotten what you have learned about calculating conditional probabilities. This is a closed book test.
A few different topics from Chapters 8, 9 and 10: St. Petersburg Paradox, Allais Paradox, and the dominance rule for decision under uncertainty. We'll be having an in-class test on Chapter 8, 9 10 on November 22. (That's the Tuesday before Thanksgiving, sorry about that.)
Continuing examination of the rationality of maximizing expected value, Chapters 8 and 9.
Test 3 due beginning of the period. We will work out a few more expected value problems and start Chapter 9 on maximizing expected value.
We will finish Chapter 8 and work expected value problems.
Test 3 is posted on the schedule page. It is a take home test and must be typed, so I have posted it as an MS Word Document. There is also a PDF in case you can't open Word and need to coopy and paste the text into a different application. Test is due 11/8. Read chapter 8 for Tuesday.
Didn't quite get to Baron on Tuesday, so we'll cover intuitive judgments of correlation and contingency on Thursday.
Read Chapter 8 from Jonathan Baron's book Thinking and Deciding, "Judgment of Correlation and Contingency" posted in Sac CT. Our 3rd test will be on Nov 3rd and cover this chapter and the two previous chapters from Hastie. Details to follow.
Read "Explanation Based Judgment." It is posted in SacCT under course material. There are two versions. The one that ends in 'A' is a smaller file of slightly lower quality. The other one is better quality, but it is a larger file and may take too long to load.
We are going to shift gears this week and read some supplementary material on the heuristics and biases people use for making probability judgments. For Tuesday Read Chapter 5 Of Rational Choice in an Uncertain World, which is entitled "Judging Heuristically." It is posted in SacCT under Course Material.
Here are the answers to the test.
Grades for the test are posted on SacCT.
Whole period devoted to test. 3/4 of the test has been uploaded to the schedule page as Test 2. The other 1/4 will be one 5 pt. problem.
We'll work through some slightly more complicated Bayes' rule examples in preparation for the test on Thursday. As before, I'll post the test on Wednesday. This time there will be 4 problems. The first will simply be to derive Bayes' rule from the definition of conditional probability and total probability. The other 3 will be to solve conditional probability problems. I will give you two of these problems to work out before class, but the final one will be new to you. It will not be the most difficult of the 3, In class I said that you could use your calculators this time, but I have changed my mind about that. Rather, I'll have one in front of the class that you can use if you like. Slides from class are posted to the bottom of the schedule page. I don't really think they are very useful if you are reading the book.
Here is the problem we didn't quite finish in class on Thursday, as well as two more. The answers are written in black type directly below each paragraph. If you scroll over them, they will show up.
You can only increase your chances of passing by studying with your friend Ray. If you study with Ray, your chance of passing goes up to 90%. You are studying for a logic exam that only 50% of students pass. (This number therefore applies to you if you don’t do something described below to increase your chances.) Unfortunately, he is not reliable. When you arrange to study with Ray, he will always say yes, but he shows up only about 25% of the time. When he doesn’t show, you are stuck studying on your own. What is the probability that you pass when you ask Ray to study? Given that you passed, what is the probability that you studied with Ray?
.6 and .38
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’s fingerprints were the only match in a database of 10,000 people deemed equally likely to have been involved in the crime prior to Fred’s positive match. 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 else ties Fred to the victim, the weapon or the scene of the crime. With fingerprints, the probability of a false positive is .01. The probability of a false negative is .07. Given the match, what is the probability that those are Fred’s fingerprints on the weapon?
.009 or about 1%
You are visiting a popular vacation island called Patay. 10% of the local population of Patay speaks English. At any given time the population of Patay is about 20% tourists. (80% are locals. Nobody is permitted to move permanently to Patay.) 70% of the tourists are English speakers. You have just met a man who calls himself David. What is the probability that he is from Patay? (You have no information at all concerning the probability that a local man will call himself David.)
Work through Bayes' Rules problems in Chapter 7. Also, answers to practice problem below is posted to the schedule page as Practice Test 2. In class we will work conditional probability problems requiring Bayes' rule, some from the book, some not.
Read the chapter on Bayes' rule and especially study the derivation from conditional probability and the formula for total probability. We will cover this in class, but for the next test (Octobrer 13th) you will need to be able to produce the derivation from memory. It is not difficult if you give yourself enough time.
The following question will be excellent preparation for the next test. It can be done based on the material through chapter 6, though last 2 are made significantly easier by Bayes' rule.
Note: wording has been changed on numbers 12 and 13.
Your upstairs octogenarian friend Charles invites his old flames Annie or Bernice over for dinner every weekend without fail. To determine who he invites on any given weekend, Charles flips a coin. If it comes up heads, he invites both. If it comes up tails, he invites one or the other, and he determines who with a subsequent flip of the coin.
Due to her rheumatism Annie comes when invited only about 60% of the time when she is the only invited guest, but when Bernice is also invited, she makes the extra effort and shows up about 80% of the time. On the other hand, Bernice , who still enjoys a postprandial romp, comes about 90% of the time when Annie is not invited, but only about 40% of the time when both are. Charles is unaware of these tendencies and he always tells each of his lady friends whether the other has been invited. (Assume that neither woman comes over unless invited. Assume that Charlie never invites any other guests.)
Calculate the probabilities associated with the following propositions for any given weekend.
1. Annie is invited to dinner.
2. Bernice is invited to dinner.
3. Annie and Bernice are invited to dinner.
4. Annie or Bernice (inclusive) are invited to dinner.
5. Annie but not Bernice is coming to dinner.
6. Bernice but not Annie is coming to dinner.7. Annie and Bernice are coming to dinner.
8. Neither Annie nor Bernice are coming to dinner.
9. Annie is coming to dinner.
10. Bernice is coming to dinner.
11. Annie or Bernice are coming to dinner.
12. Given that Annie alone is invited, she is coming to dinner.
13. Given that Bernice alone is invited, she is coming to dinner.
14. Given that Annie came, Annie alone was invited.
15. Given that Bernice came, Annie and Bernice were invited.
We will finish working through the important derivations in Chapter 6 and look at a couple more conditional probability problems before moving on to Chapter 7 and Bayes' Rule.
We will look at some of the more complicated problems at the end of Chapter 5, and then do Chapter 6 which formalizes and generalizes the basic rules of probability.
Grades for Test 1 have been posted to SacCT.
Test 1 covering chapters 1-5 and supplementary material. There is now a link to the test on the schedule page. You must reproduce answers in class without aid of book or notes. Mathematical calculations are elementary, so no calculators either.
Read Chapter 5 on conditional probability and work through the examples.
Here's a roll call question for you to work out before class.
You are lying in bed and someone (one and only one) is on the porch. You know it has to be either Bob, Harold, or Judith, and it is equally likely to be either one. Bob always rings twice. Harold always rings once and knocks once (no particular order). Judith always knocks twice. Bob and Harold are creeps, you only want to see Judith. There is a knock at the door. How likely is it to be Judith?
We will review the material of Chapter 4 and work though some of the basic probability problems in the book. Next Thursday 9/22 we will have our first in-class test covering chapters 1-5 and the supplemental readings. It will be closed book and notes. I will put a copy of this test online by Wednesday.
Here is a problem for you to work out for roll call.
You and your friend are trying to get free tickets to see Vampire Weekend. The chance involves a lottery where there is a surprisingly high 1 in 10 chance of getting a ticket. To get into the lottery all you need to do is sign up online. Assume that each person can only do this once and you aren't going to try to cheat. You both agree that if one of you wins a ticket you will flip a coin to see who gets to go.
What is the probability that you will get to go?
9/8/11 & 9/13/11
No class meeting on Thursday. Read through chapter 4. Read the Wikipedia article on Regression Toward the Mean and then read Noah Lehrer's article "The Truth Wears Off," and listen to the WNYC Radiolab interview of Jonathan Schooler (who is featured in Noah Lehrer's article). After doing all this ask yourself whether you think regression toward the mean is an adequate explanation of the decline effect or whether something spookier is going on.
Read chapter 3 and do the exercises (all are answered in the back of the book.)
Read The Cancer Cluster Myth.
Read Chapters 1 and 2 and watch The Drunkard's Walk. There is a hyperlink to it on the schedule page.
Read the syllabus
Read Chapter 1 of the text.