# 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 difficulties.

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 class.
• 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)