The format of the final will somewhat similar to those of the in-class exams. You may use calculators, but not books, notes, etc. I anticipate that part of the final will be short multiple choice problems, and the rest will be some what longer "work it out" problems, similar in spirit to what you've encountered on the in-class exams and the homework.
If you questions regarding any of the topics we've covered that you'd like to discuss, be prepared to ask them in class on Thursday, May 6, or preferably email me beforehand. I anticipate being available for questions in my office on Monday, May 10 and Wednesday, May 12 in the mornings.
In addition to material covered on the in-class exams, the final will also cover:
Chapter 7 Normal random variables (Section 7.2) and Exponential random variables (Section 7.3). As with other (continuous) RVs, you should know or be able to quickly derive the density function, the distribution, and expectation and variance of these RVs. Also, be aware of when these RVs are relevant (e.g., the time between earthquakes for the exponential RV, etc.), be able to translate questions about normal RVs to ones about standard normal RVs, and be prepared to use them in various contexts. (I won't ask you about the Gamma distribution (Section 7.4) on the final.)
Chapter 8 Bivariate Distributions (Sections 8.1 - 8.3). We now consider two or more RVs together. You need to know joint probability mass
(discrete case), density (continuous case), and distribution functions. Know how to compute probabilities
using them - this will involve multiple integrals in the continuous case. You should also
know how to compute probabilities involving only one of the random variables from the joint functions
(i.e., the marginal probability mass/density functions). Similarly, you should be familiar with
the conditional mass/density functions. You should also know what it means for RVs to be independent, and how expectations behave in this context (see Theorems 8.5 and 8.6 on pages 332 and 333).
Chapter 9 Multivariate Distributions (Section 9.1). The ideas from Chapter 8 are extended to n > 2 random variables.
Chapter 10 Expectations of sums of random variables (Sections 10.1).
Be comfortable working with the important fact that expectations are linear in various contexts (see Theorem 10.1, its corollary, and the examples in this section).
Chapter 11 Sums of independent random variables (Section 11.2) and the Central Limit Theorem (Section 11.5). Be aware that sums of independent binomial RVs are binonial, sums of independent Poisson RVs are Poisson, sums of independent normal RVs are normal... The only formulas for sums of independent RVs that I will expect you to know are the
one for normal RVs (Theorem 11.6), which is used frequently in word problems (like those ``bowling'' examples), and the one for binomial RVs (Theorem 11.4), which is intuitively clear.
Know the Central Limit Theorem and how to use it in word problems to
approximate probabilites in various contexts (as done in class, see, e.g., the last WeBWorK assignment).
Some potentially relevant review problems from the ends of the chapters (in the 3rd edition of the text):
Chapter 7 (page 308): #2, 5, 8, 9, 11 (1, 3 were suggested prior to Exam 2)
Chapter 8 (page 365): #1, 3, 6, 11, 15, 21
Chapter 9 (page 398): #1, 4
Chapter 10 (page 454): #1, 2, 3
Chapter 11 (page 507): #1, 11, 14, 17, 18
Solutions to the odd numbered problems may be found in the back of the text.
You may also find the homework, the WebWorK assignments, and the in-class exams useful for studying. Answers to the problems on the in-class exams are available from the course homework page. All WeBWorK assignments will remain open until the final.