Chapter 1
Probability Theory
“If any little problem comes your way, I shall be happy, if I can, to give you a hint or two as
to its solution.”
Sherlock Holmes
The Adventure of the Three Students
1.1 a. Each sample point describes the result of the toss (H or T) for each of the four tosses. So,
for example THTT denotes T on 1st, H on 2nd, T on 3rd and T on 4th. There are 2
4
= 16
such sample points.
b. The number of damaged leaves is a nonnegative integer. So we might use
S
=
{
0
,
1
,
2
,...
}
.
c. We might observe fractions of an hour. So we might use
S
=
{
t
:
t
≥
0
}
, that is, the half
inﬁnite interval [0
,
∞
).
d. Suppose we weigh the rats in ounces. The weight must be greater than zero so we might use
S
= (0
,
∞
). If we know no 10dayold rat weighs more than 100 oz., we could use
S
= (0
,
100].
e. If
n
is the number of items in the shipment, then
S
=
{
0
/n,
1
/n,.
..,
1
}
.
1.2 For each of these equalities, you must show containment in both directions.
a.
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 Spring '12
 Dr.Hackney
 Statistics, Probability, Natural number, Distributivity

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