Chapter 1, Real and Complex Analysis, Third Edition, Rudin, W., 1987.
The homework at the end of the chapter is very useful for supplemental learning for Chapter 2 in the Lecture Notes (LN). Specifically, Problem 4 (on topology) can be done before reading LN Chapter 2; Problems 1 (on sigma algebras and set cardinality) and 11 (on set theory, measure space, and convergent series with nonnegative terms) can be done after reading LN Sections 2.1 and 2.2; Problems 2, 3 and 5 (all on measurable function concepts) can be done after LN Section 2.3.1; Problems 6 (on measurable functions and integrals) and 13 (on integration of nonnegative functions) can be done after LN 2.3.2; and the remaining problems, 7 (on the Monotone Convergence Theorem), 8 (on Fatou’s Lemma), 9 (on Fatou’s Lemma and the Dominated Convergence Theorem), 10 (on properties of integrals and uniformly convergent sequences of functions) and 12 (on integrability and L1-space) can be done after LN Section 2.3.3.
Dr. Emil Cornea has provided a proof for the formula for the density of the non-central chi square distribution presented on Page 10 of the Lecture Notes. Recall in this case that the scale parameter for the gamma density is the reciprocal of the usual parameter. Dr. Cornea’s Proof.
Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society Series B, 44:226-233.
This classic paper, which can be downloaded from JSTOR, shows how to compute the variance of estimators using EM.
Sundry Lecture: Random Thoughts
Homework #1: Problems 2, 6,
11, 12 and 14 in Lecture Notes Page 13.
Due Wednesday, August 30, at the beginning of class. Solution to Homework #1.
Homework #2: Problems.
Due Wednesday, September 13, at the beginning of class. Solution to Homework #2: (Part 1, Part 2).
Homework
#3: Problems 7, 10, 12 and 13 in Lecture Notes Page 39.
Due Wednesday, September 20, at the beginning of class. Solution to
Homework #3.
Homework
#4: Problems 11 and 17 on Page 40 and Problems 1, 2 and 3 on Page 76 in Lecture
Notes.
Due Wednesday, October 4, at the beginning of class. Solution to
Homework #4.
Homework
#5: Problems 4, 5, 6 and 7 in the Lecture Notes Page 76.
Due Wednesday, October 11, at the beginning of class. Solution to
Homework #5.
Homework
#6: Problems 8, 13, 16 and 17 in the Lecture Notes Page 76.
Due Wednesday, October 18, at the beginning of class. Solution to
Homework #6.
Homework
#7: Problems 10, 12 and 18 in the Lecture Notes Page 76.
Due Wednesday, October 25, at the beginning of class. Solution to
Homework #7.
Homework
#8: Problems 1, 2, 3 and 5 in the Lecture Notes Page 104.
Due Wednesday, November 8, at the beginning of class. Solution to
Homework #8.
Homework #9: Lehmann and
Casella: Page 134, Problem 2.25; and Page 136, Problem 3.23. Lecture Notes:
Problems 2 and 3 on Page 126.
Due Wednesday, November 15, at the beginning of class. Solution to
Homework #9.
Homework #10: Problems 4, 5 and 6 in the Lecture Notes Page 126.
Due Wednesday, November 29, at the beginning of class. Solution to Homework
#10.
Homework
policy: unless you have a special situation approved by both the instructor and
grader, 50% of the total points will be automatically taken off from any late
homework (late homework means it was turned in after class on the due date). In
case you are unable to attend a class, please leave your homework in my mailbox
prior to class or ask someone else to turn it in for you.
Please follow and uphold the UNC honor code. We will follow
the approved process of handling violations. Please review the
honor code system.
The first midterm (Midterm I) will be on Wednesday, September
27. The class time on Monday,
September 25, will be devoted to review for the
midterm: please come to class that
day prepared with 2-3 meaningful questions to ask regarding material covered on
this midterm. The corrections for
Midterm I are due Monday, October 9. The exam and answer key will
be made available on about October 4. The content for this exam covers
Chapter 1 and Chapter 2 of the Lecture Notes. The exam and solution for Midterm
I for 2009 are here: exam and solution; for 2010: exam
and solution;
for 2011: exam
and solution;
for 2012: exam
and solution;
for 2013: exam
and solution;
for 2014: exam
and solution;
for 2016: exam
and solution;
and for 2017: exam
and solution.
Some practice problems here and solution here.
Note: Take home extra credit (problem 2(e)) due with homework this coming Wednesday (October 4): this is open book but with work done individually. Midterm corrections (done individually) due with homework on Wednesday, October 11.
The second midterm (Midterm II) will be on Wednesday, November 1. The class time on Monday, October 30, will be devoted to review for the midterm: please come to class that day prepared with 2-3 meaningful questions to ask regarding material covered on this midterm. The content for this exam covers Chapter 3 of the Lecture Notes. The exam and solution for Midterm II for 2009 are here: exam and solution; for 2010: exam and solution; for 2011: exam and solution; for 2012: exam and solution; for 2014: exam and solution; for 2016: exam and solution; and for 2017: exam and solution.
Prior to 2009, there was only one midterm in Bios 760 which covered Chapters 1 and 2 and Section 3.1 of the Lecture Notes. Midterms and solutions for several previous years and a set of practice problems for these midterms with solutions can be downloaded:
2006 Midterm with its solution, Midterm 2007 with its solution, Midterm 2008 with its solution, and Practice Problems with its solution.
The final exam is on Monday, December 11, at 12:00-3:00PM, in our regular class room (HC 0001). The final exam covers Chapters 4, 5 and 6 of the Lecture Notes. The class time on Wednesday, December 6, will include a review for the final: please come to class that day prepared with 2-3 meaningful questions to ask regarding the material covered on the final. The exam and solution for the final exam for 2009 are here: exam and solution; for 2010: exam and solution; for 2011: exam and solution; for 2012: exam and solution; for 2013: exam and solution; for 2014: exam and solution; and for 2016: exam and solution.
Prior to 2009, the final exam covered Chapters 3, 4 and 5 of the Lecture Notes. Some practice final exams and solutions for this period can be downloaded:
2006 Final (Solution), 2007 Final (Solution), and 2008 Final (Solution).