Information Pertaining to the Final Exam
Basics
The exam is due at 10:15 PM on Monday, May 18.
The exam is an open books and open notes exam,
but you cannot share books or notes during the exam.
Between the time I make the exam available and the time the exam is due, you should not communicate with anyone about the exam problems, or course material in any way
related to the exam problems.
You can use a calculator and/or computer during the exam if you wish to.
(Some may wish to use software such as Maple, Mathematica,
or Wolfram Alpha, a digital copy of the text, or the course web site.)
What to Study
While some basic concepts from the first five chapters (that were covered on the two midterm exams) may be useful,
the final exam will focus on Ch. 6 through Ch. 8 of the text, and the vast majority of the points will be for
Ch. 6 and Ch. 7 type problems.
My advice is to first quickly look over the highlights from each chapter that I list below, paying extra attention to the few items in bold font.
(Hopefully a lot of these things will seem very familiar.) Then turn your attention to the list of homework problems given at the bottom of this web page.
If you can get comfortable with the problems and examples indicated below, then you ought to be able to do well on the final exam. (Some of the exam problems are rather similar,
but even a bit easier, than the homework problems listed. (If you're short on time, it may be best to just focus on the list of homework problems found below, as well as the examples from the class notes that I have referred to below, and not worry about looking at everything from the book that I list here.))
Chapter 6
- formulas for obtaining marginal pdfs from a joint pdf, p. 241 (3rd line from bottom) & p. 242 (top line);
Example on p. 6-5 of the class notes, Example on p. 6-6 of the class notes
- obtaining probabilities using a joint pdf, Example 1d, p. 242; Example on p. 6-4 of the class notes
- using "cdf method" to obtain pdf of a function of two r. v's from a joint pdf, Example 1f, pp. 244-245; Example on
p. 6-7 of the class notes; Example on p. 6-9 of the class notes; Example on p. 6-12 of the class notes
- formula for conditional pdf, p. 270;
Example 5a, p. 271; Example on p. 6-16 of the class notes
- obtaining cdf and pdf of sample minimum and sample maximum, pages 6-18 and 6-19 of the class notes; Example on pages
6-19 and 6-20 of the class notes
- the method emphasized in Sec. 6.7 won't be needed for the final exam (although you could
use it for one of the parts (but I don't think it's the best way to approach that part (with the "cdf method" being perhaps the best way
to address the part)))
- parts (b), (c), (d), (e), and (f) of Problem 6.9 on p. 292
- Problem 6.19 on p. 293
- Problem 6.22 on p. 293 (and additionally obtain the covariance of X and Y from this joint pdf (a Ch. 7 task))
- Problem 6.52 on p. 295
Chapter 7
- Examples on pages 7-2 and 7-3 of the class notes (note there is more than one way to get the expected value of a sum of r. v's)
- Example 2e through Example 2j, pp. 307-310
- Example of p. 7-6 of the class notes
- Example of p. 7-8 of the class notes (but don't worry about the part that continues on p. 7-9)
- alternate formula for Cov(X,Y), top portion of p. 329 (below Definition); Example near middle of p. 7-10 of the class notes
- variance of a sum of r. v's, (4.1) on p. 330;
Example 4b, p. 332; Example on p. 7-12 of the class notes
- correlation of 2 r. v's, bottom of p. 7-14 of the class notes; Example at bottom of p. 7-15 of class notes
- conditional expectation, pp. 337-338;
Example 5b, p. 338; Example near middle of p. 7-17 of the class notes
- computing expectations by conditioning, p. 315;
Example 5d, pp. 340-341; three Examples on pages 7-18 and 7-19 of the class notes
- mgfs, pp. 360-365;
1st two Examples on p. 7-24 of the class notes;
two Examples on p. 7-25 of the class notes
- mgfs of sums of independent r. v's (and identifying the distributions of the sums), bottom of p. 364;
Example 7f,
Example 7g, and
Example 7h, pp. 366-367; three Examples on p. 7-28 of class notes
- part (a) of Problem 7.9 on p. 378
- Problem 7.13 on p. 379
- Problem 7.22 on p. 380
- Problem 7.30 on p. 380 (can be solved in several ways)
- parts (a) and (b) of Problem 7.50 on p. 382
- Problem 7.52 on p. 382
Chapter 8
- Although the various inequalities and laws of large numbers are important results, they don't necessarily lead to
good exam problems. So for this chapter you can just get by with knowing how to obtain approximate probabilities using the
central limit theorem. (See the first two examples on page 8-6 of the class notes (but don't worry about the
last example on p. 8-6).)
14 good homework problems/parts to review
(with the 11 most important ones in bold font).
- Problem 4, HW 8 (note that the normal approximation of a binomial distribution probability is a special case of using the CLT approximation)
- Problem 7, HW 8
- part (a) of Problem 8, HW 8
- part (b) of Problem 8, HW 8
- part (a) of Problem 3, HW 9
- part (b) of Problem 3, HW 9
- Problem 2, HW10
- Problem 3, HW10
- Problem 5, HW10
- part (a) of Problem 5, HW 11
- part (a) of Problem 1, HW 12
- part (b) of Problem 1, HW 12
- Problem 2, HW12
- Problem 4, HW12