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Supplementary problems in Math 2030 (Elementary Probabilty)
The homework assigned should be thought of as the minimum number of problems
that you'll need to complete. Unless you find you can breeze through the
homework, you would be well advised to attempt additional problems, talk
them over with your friends, and ask me or the TA about them (in or after
class, the problem sessions, or during office hours) if you have
Many of the sections we have looked at have additional topics that I will
not discuss in class, or that I will be coming back to later. The following
is meant to be a rough guide to the problems in those sections that deal
with this additional material. To do those problems, you would have to read
those parts of the text on your own.
Section list (as of Feb 16, 1997)
Chapter 1: You should be able to do all the problems by now, though some of
them involve topics that I didn't emphasize as much as in the text.
2.1: I didn't discuss the "mode" of the binomial distribution. Unless you
read the text's discussion of this topic, you shouldn't try problems
8, 91, 11a, 15.
2.2: Problems 15-17 have little to do with the material I discussed in
Review exercises from section 2:
If you try these exercises, be warned that one of the things you would have
to decide in each problem, is whether binomial probabilities should be
evaluated exactly, or approximated using the normal or Poisson
approximations. We have not covered the latter approximation. Basically the
normal approximation is good when P(X=k) is small for each k. In other
words, when the mean number of successes (ie np) is fairly big. When P(X=k)
is not always small (ie, np is not all that big, even though n is), one uses
the Poisson approximation. You should check for this in the problems, and
not worry about completing the ones in which this turns out to be the case.
3.1: The lectures give the background for the following problems:
1, 3, 5, 7, 8, 9, 14a-d, 18, 19a-c, 23, 24
Review exercises from section 3:
I wouldn't try these yet. Virtually all of the problems require material
we haven't yet covered, at least somewhere.
4.1: Problems that require material not yet covered in class are:
2bc, 3e, 4bc, 5d, 9
4.4: We didn't discuss the METHOD which the book discusses in this section.
However, all the problems in the section can be worked out using
distribution functions, as we did in class. To do problems 1 and 3, you'd
have to look up the form of the exponential and gamma densities.
4.5: Problems 8 and 9 go beyond what we've done in class. The other problems
should be OK, though again you'd have to look up the form of the exponential
density for some of the problems (and the "geometric" distribution of b)