Math 361 X1
Exam 3 Study Guide
Friday, May 2, 12 - 1 pm, 260 MEB
Rules
The usual rules apply: No calculators, books, or notes.
You can and should leave answers in "raw" form - e.g., leave binomial
coefficients unevaluated except in the simplest cases.
A normal table will be distributed.
Exam content
The exam will be on the material covered in class since the last exam,
excluding joint continuous distributions. In the Pitman text,
this roughly corresponds to Chapter 4 and Section 3.3 (normal
approximation, which did not make it into the last exam), excluding
those sections and topics that were not covered in clas. Below is a
more detailed syllabus. (See also the Reading
Guide for a detailed listing of sections and topics that you should
know, along with recommended examples and practice problems.)
- 3.3 Variance, standard deviation, normal approximation:
Skip the parts on tail probabilities (p. 191),
Chebyshev's inequality (P. 192 - 193), and skewness (p. 198).
The most important part of this section, and one
of the most important topics of this course,
is normal approximation for sums of independent random variables.
Refer to the handout
Normal Approximation, II
for the relevant formulas that you are expected to know.
A normal table (the same as the one given in the book and also handed
out in class) will be provided.
- 4.1 Continuous distributions:
Skip p. 272 - 275. See the handout Continuous
Distributions for a list of formulas that you should know. These
include general formulas and properties of continuous distributions,
as well as formulas associated with three particular distributions,
uniform, normal, and exponential. (The latter set of formulas can also
be found in the distribution summary on p. 477.)
- 4.2 Exponential distribution:
Skip the material on the gamma distribution (essentially, p. 285 -
292). You need to know the Poisson process, its properties, and the
various random variables associated with the Poisson process.
- 4.3 Hazard rates: Skip this section.
- 4.4 Change of variables:
You can skip the main body of this section, and in particular the
change of variables formula given in this section, since we did not
cover this formula in class. In class (and in hw problems - e.g.
5b of HW 9) we used a different, safer, and more widely applicable
method (which consists in finding first the c.d.f. of the new random
variable, then differentiating to get the density)
that serves the same purpose, and you should be familiar with this
method.
- 4.5 Cumulative distribution functions:
The concept of a c.d.f., was introduced in class at an earlier stage,
along with that of a density function (see 4.1),
and was covered in several class examples and HW
problems. C.d.f.'s are fair game for the exam.
You can skip p. 320 through the remainder of this section.
- 4.6 Order Statistics: Skip this section.
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Last modified Fri 25 Apr 2003 05:20:42 PM CDT