Assignment #1
Note:
Homework exercises are not handed in. However, homework is strongly stressed
on the exams. Most of the exam problems will be similar to homework exercises.
Reading:
All of Chapter 1 and Section 2.1.
Exercises:
A1, A2, A3 (do these first after reading “Review of Formulas ...”)
1.1, 1.2(a,b,d), 1.4, 1.5, 1.6, 1.10, 1.13, 1.17, 1.18, 1.19, 1.20, 1.21, 1.22, 1.23, 1.24, 1.25,
1.26, 1.32, 1.33, 1.34, 1.36, 1.37, 1.38, 1.39, 1.41, 1.44, 1.46, 1.47, 1.51, 1.52, 1.53, 1.54, 1.55
B1 – B8 (do these as the corresponding topics are covered in lecture)
2.1 – 2.9
Some Comments:
1.2, 1.10
Do 1.2(a,b,d) and 1.10 from first principles as in the proof of Theorem 1.1.4 on pages
3 and 4.
1.3, 1.14
You should also read exercises 1.3 and 1.14 and know the results in these exercises.
1.20
Assume the 12 calls are distinct (say, they are from 12 different friends) so that there
are 7
12
equally likely possibilities. Another way to think of this problem is to suppose
you have 12 friends and each calls you on a day selected at random. This allows you
to use the principle of inclusionexclusion to solve the problem. This solution is easier
than the one in the solution manual.
1.32
The statement of 1.32 is murky and I believe the solution in the manual is wrong.
What they are asking for is the following: The
N
candidates are interviewed in a
random order.
Suppose the
i
th candidate you interview is the best one you have
seen so far. What is the (conditional) probability this candidate is the best overall?
Assume there are no ties among the candidates, that is, there are no candidates that
are rated the same. The correct answer is
i/N
.
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Review of Formulas from Introduction to Probability
•
X
denotes a random variable (rv).
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 Fall '10
 Frade
 Probability, Probability theory, probability density function

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