W 11/3 -- Went over the exam for about a third of the class,
and spent the rest talking about changes of variable from the point
of view of ``first principles". That is, I find that it's almost
always easier to compute P(g(X) < y) by looking at it directly, rather
than by remembering a formula. The most complicated example was the
distribution of X^2, when X is uniform on [-2,3]. I also
passed out
HW9
.
F 11/5 -- Discussion of the cumulative distribution function,
and also how to think about the maximum and minumum of a set of
independent random variables, and the formula that, if X is a
non-negative random variable with finite expectation, then E(X) is the
integral of P(X > x) as X runs from 0 to oo.
M 11/8 -- I passed out HW9 solutions
, and talked about several of the problems. The solution given
there for problem 4 has several errors. I then began with
§ 5 from the book.
W 11/10 -- I passed out more
on HW 9, which includes a corrected solution to problem 4. More
discussion of §5.1,2. At the end, I passed out
HW10
.
F 11/12 -- Some review of what we had done in Chapter 5 to date,
some answering of questions about HW10, some discussion of the "Parental
Notification" issue. A hodge-podge, but those who were there felt it
was worthwhile.
M 11/15 -- A bit more than half the class was spent going over the HW10 solutions
, and the rest was devoted to a proof that linear combinations of
independent normally distributed random variables are also normally
distributed. At the end, I passed out
HW11
.
W 11/17 -- Another 20 minutes talking about HW10, with a review
of integration in the plane which evidently should have been done
sooner. More on the sum of two independent normal random variables,
and some related word problems worked in detail. For those of you who
plan to turn in the homework on Friday, the Gamma distribution is
discussed in § 4.2 and will be covered in class on Friday.
F 11/19 -- An attempt to finish up § 4, 5. Discussion of the
Gamma distribution and more examples, based on class
request. Presentation of book problem 5-4-11.
M 11/22 -- More review. Several homework problems gone over,
and an explanation of the significance of the Gamma(1/2,lambda)
distribution: if X is standard normal, then X^2 is Gamma(1/2,1/2).
Passed out: HW11 solutions
and HW12
.
M 11/29 -- A review of Homework 11, plus coverage of § 6.1, 6.2. This material is largely intuitive and much has already been covered in class.
W 12/1 -- Some hints for Homework 12, plus coverage of § 6.3.
Formulas were presented which allow one to avoid double integrals in
compution the distribution of X + Y, etc. There was some
discussion of whether these were easier or harder.
F 12/3 -- Passed out: HW12 solutions
. I talked about HW
12 and some of § 6.4 about correlation and covariance.
Only 10 of 23 in class when the bell rang. I said I needed 17 to
distribute the ICES forms and get a meaningful return. The 17th person
walked in around 11:20, and the forms went out at 11:40.
M 12/6 -- Review for the Third Exam
W 12/8 -- Third Hour Exam.
F 12/10 -- Third exam returned; last day of instruction.
S 12/11 -- Reading Day: Office Hours 10:30 am -> 12:30 pm and
2:00 pm -> 4:00 pm
F 12/17 -- Final Exam, 8:00 -> 11:00 am.