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F 12/1/06
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No class.
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M 12/4/06
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HW due: Reading assignment (1 paragraph) and problem set on
a priori probability.
In class: Grading and correction of assignment.
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T 12/5/06
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HW due: Write #6.37, 6.39, 6.38, 6.40, 6.58, 6.60, 6.65; read
6.66. On Tuesday I would like to dive right in to #6.66 without having to
spend any class time getting everyone up to speed on the background of the
problem.
Note 1: The answers in the back of
the book are not totally correct for these problems, and they do not show the
Venn diagram required in #6.39.
Note 2: Please use the notation ~A
instead of Ac for the complement of event A.
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W 12/6/06
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HW due: #6.66 done 4 ways, as follows.
1. Do the problem as posed in the text. I strongly recommend using 100,000
(or a million) people at the top of the tree diagram instead of probabilities
as shown on p. 353. The reason is that counts of people are much easier to
work with, computationally speaking, than decimal probabilities.
2. Let the incidence (given as a notional 1% in the text) be replaced by the
parameter H (for “HIV antibody
probability). Remember, a parameter in mathematics is an adjustable constant that captures some aspect of the problem that
we may wish to vary. Then re-do the tree diagram, taking the parameter H into account. Develop an algebraic
expression for PPV in terms of H.
If you have forgotten what PPV is, review your class notes from yesterday or
look it up on the Internet.
3.(a) Use your answer to #2 to find PPV for HIV infection rates of 0.5%, 1%,
1.5%, 2%, 5%, 10%, and 15%. Note:
If you did #2 correctly, your answer for the PPV when incidence is 1% should
match your answer for #1.
(b) Write one sentence explaining why Mr. Hansen thinks
that a good math curriculum should always include teaching students how to
develop parameterized solutions.
4. Recopy the 35-word statement in parentheses in #6.66(c) on p.364, exactly
as it is worded there. The purpose of this exercise is to reinforce one of
the more important things you should learn this year.
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Th 12/7/06
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HW due: Read this
article from ABC and be prepared to discuss it. That should not take too long.
Use your remaining time to finish up yesterday’s HW assignment.
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F 12/8/06
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HW due: A previously assigned HW set was to be collected
and graded (20 pts.) at the start of class. However, I decided to postpone
this until Monday since we had a pop quiz instead.
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M 12/11/06
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HW due: Read this
article from the Post and
answer the following comprehension questions.
1. Which type of probability, a priori
or a posteriori, are insurance
companies most concerned with? Explain your answer.
2. Why are acts of war and acts of terrorism not covered by most insurance
policies?
3. What are reinsurance companies?
Also, be prepared to discuss both this article and the one from last
Thursday. The HW collection originally scheduled for Friday will occur this
time. As always, if you are absent, you must make up these assignments on
your own time.
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T 12/12/06
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HW due: Answer the following questions.
1-3. Prepare three (3) questions that you think would be likely to resemble
those that you will see tomorrow. If you do not have time to write entirely
original questions, you may cite up to two questions from your textbook, the
Barron’s AP review book, or Mr. Hansen’s a priori problem
set. (Give source, page number, and question number.) However,
at least one of your questions must be your own creation.
For questions 4-8, assume that St. Sopher’s [sic] Cathedral is having a
raffle in Feb. 2007. There will be 1000 tickets sold for $100 each, but
unlike the St. Sophia’s raffle, this one will be strictly for cash. All
prizes will be awarded in such a way that the recipient’s after-tax winnings
equal the stated value. (For example, if a person in the 33.75% bracket wins
a $500 prize, the actual payout will be $754.72, so that after the tax of
$254.72 is deducted, the winner will still have a solid $500 cash prize.)
There are to be two $500 prizes, two $1000 prizes, a $5000 prize, and a grand
prize of $25,000. Answer the following questions, showing your work:
4. Compute the expected after-tax value of a ticket. Why is this value less
than $100?
5. Neglecting the tax payments made by St. Sopher’s, what is the total value
of prizes that the church must pay out?
6. If all recipients are in the 33.75% bracket, and if promotional and
administrative expenses are $7500, what is the cathedral’s net profit from
the raffle?
7. What is the probability that a ticket is a grand prize winner, given that
it is a winner?
8. What are the odds against winning a prize?
9. Name a current game show (other than a poker game) that makes heavy use of
conditional probability.
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W 12/13/06
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Quest (70 pts.) on Probability. This will cover everything discussed in class from
Nov. 10 through yesterday: simulations, a
priori probability, expected value, odds, PPV, and standards of proof.
You will also need to know what a reinsurance company is, but there will be
no “Quick Study” or other recent article reading tested.
Study Aids: You may find the a priori problem set and solution key to be useful.
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Th 12/14/06
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HW due: Rewrite your entire quest
from yesterday, even the problems that you think you did correctly. I
have not yet made a decision regarding scoring. I am well aware that
yesteday’s testing conditions were far from ideal.
Honor Code Notice: You may work
with other students. However, you may not copy another student’s work. All
work must be your own. A good guideline is to make sure that whenever your
pencil is in motion, your eyes are on your own paper, not someone else’s
paper. If you work in groups, all members of the group must participate.
“Leeches” or “lurkers” who piggyback on other people’s work without
contributing anything substantial of their own are cheating as far as this
assignment is concerned. Knowingly allowing someone to be a leech is also an
honor issue. Don’t let anyone look at your homework paper unless you are
standing right there. Suppose someone says, “Say, could I borrow your paper
for a while?” Your response to him should be
(A) “Sure! I always support my fellow student.”
(B) “Sure! I don’t know if this will help you, but feel free to borrow it and
look it over.”
(C) “Sorry, I don’t ever work with other students.”
(D) “Let’s ask Mr. Hansen what he thinks.”
(E) “That’s an interesting question. Is there a time we can sit down and work
together on this assignment?”
Answer: E. (E is better than D because
it shows more proactivity.)
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F 12/15/06
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HW due: Attend the Service of Lessons and Carols on
Thursday night (expected of everyone).
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