1, 3, 15, 17, 23, 25 Note: 15, 17, 23, and 25
were only intended as important review of
differentiation, not as practice with key concepts for
the test.
1, 3 (don't agonize -- there will be no trigonometric
functions on the test), 7, 11,
13, 15, 17Added: 9 Note:
any tricky graphs will be provided for you on the
test but you should know how to interpret them.
1, 3, 5, 7, 9 Update The Newton's Cooling
Solution (notes 185) was updated to fix a mistake
(01/25/10). The corrected version introudces u
in a change of variables.
1, 3, 25, 27 Note: don't agonize over these or
waste a lot of time on the graphs -- just look at the
answers and be sure that you understand. Also, the main
point of asking 25 and 27 was to have the results
available for the corresponding questions in the next
section.
11, 15, 27, 29Note: again, don't
agonize or spend a lot of time on making graphs -- just
look at the answers and convince yourself that you could
do it.
1, 7, 9 (ignore "counting" part of question), 11 (ignore
"counting" again)
DANGER! I made two pencil-o's (like a type-o,
but with a pencil) when I prepared my notes: one
on page 221 and one
on page 223 (both the
figure and
the formula).
These mistakes have been fixed before posting
here. All posted version are correct.
1, 3, 9, 11 (ln(e) = 1), 13 (for expectation, see
6.7-15), 15 (the "inequality" is just that the
geometric mean should always be less than the arithmetic
mean, which is just the usual average), 17
1 (ignore "range" and "computational formula" part),
3, 5, 9 (integrate the PDF to get the CDF,
set the CDF equal to 0.25, 0.5 and 0.75 to get the
quartiles) 11, 13, 15
Sectond Test:
The class average was 41/50 points.
Hints: You might wisht to compare
the hints to the
test key.
Key: You can use the
answer key to review
the grading for mistakes.
9 (write down L(p) for b(k; n, p) with k = 2, n = 4,
then plug in p = 0.5), 15 (notes 291--292, repeat the
binomial maximum likelihood derivative for n = 6 and k =
5 to find the maximum likelihood p value, then compute
E(W) = ($1)P(W = $1) + (-$6)P(W = -$6) to get the
average, were random variable W represents winings from
betting on the game)
The final examination will begin at 8:00 AM on Friday
the 30th of April, in JFB 102 (the same room as for
class). The final will last for two hours.
Final Examination Hints:
The exam will have one question for each of the
first three chapters (5, 6 and 7) plus three more
questions for the last chapter (8). You will be
asked to solve only five questions, of your
choice, whichever questions you like best.
As you can see in
this hint,
the question for chapter 5 will be about phase
planes. I will review this during as part of a
review session during class on Wednesday, the 28th
of April. UPDATE: the hints were updated at
7:11 PM on the 27th of April.
Problems from chapter 6 will involve some
combination of concepts from questions 4 and 5 of
the second test. It will not be my intention to
ask about any other topics from that test, beyond
the fact that all math topics are somewhat
interrelated. The relevant hints are 12, 13, 14,
15, 19 and 20 but only for the continuous
case. It was simple integration that gave people
the most trouble. I will be looking for people to
do better in this area. A review of hint 3.b from
the first test is advisable.
Problems from chapter 7 will involve some
combination of concepts from questions 3, 4 and 5
of the third test so hints 4, 5 and 7 are
relevant. Since question 4 saw no love the first
time, it is the most likely candidate for
recycling but it's not that hard. Check the key.
Though not tested directly, the rules for adding
expectations and variance might prove indirectly
useful.
Here are
the hints for
final chapter of the book. I do not promise that
the hints cover every minor topic explicitly but
major topics not covered in the hints will not be
on the final
examination. UPDATE:
The wording of the hint was improved, a little a
12:26 PM on the 28th of April.
DANGER! You must take the final. Do not make
plans to leave town before the date of the final.
