Chapter 1 Homework; FALL 2011
1. Consider the following CM: A 10sided die
is tossed, with faces marked 1, 2, . . . , 10.
The outcome is the number on the face that
lands up.
(a) Determine the sample space.
(b) List the elements of the following
event:
A
=
the outcome is an odd
number.
(c) List the elements of the following
event:
B
=
the outcome is an even
number larger than 6.
(d) Describe
the
following
event
in
words:
C
=
{
7
,
8
,
9
,
10
}
.
2. Refer to the previous exercise. Assume the
ELC. Calculate the probability of each of
the events,
A
,
B
and
C
.
3. A CM has a sample space that consists of
five outcomes: 1, 2, 3, 4 and 5. For each of
the following assignments, decide whether
it is a mathematically valid way to assign
probabilities for this situation. If not, ex
plain why not.
(a)
P
(1) = 0
.
30
, P
(2) = 0
.
15
, P
(3) =
0
.
25
, P
(4) = 0
.
20
, P
(5) = 0
.
10
.
(b)
P
(1) = 0
.
30
, P
(2) = 0
.
15
, P
(3) =
0
.
20
, P
(4) = 0
.
20
, P
(5) = 0
.
10
.
(c)
P
(1) = 0
.
30
, P
(2) = 0
.
15
, P
(3) =
0
.
25
, P
(4) = 0
.
20
, P
(5) = 0
.
20
.
(d)
P
(1) = 0
.
30
, P
(2) = 0
.
15
, P
(3) =
0
.
25
, P
(4) = 0
.
40
, P
(5) =

0
.
10
.
4. Refer to the previous exercise. Use assign
ment (a) to calculate the probability of each
of the following events.
5. Refer to the previous exercise.
(a) Verify that:
P
(
B
or
D
) =
P
(
B
) +
P
(
D
)
.
(b) Verify that Rule 6 is true for events
B
and
D
.
(c) Given that
P
(
B
) = 0
.
15 + 0
.
20 =
0
.
35
,
explain why you know that
P
(
A
)
=
0
.
65
without adding the
probabilities of outcomes 1, 3 and 5.
(d) Of the five events listed in Exercise 4,
find all pairs that illustrate Rule 5.
6. You are given the following information:
the events
A
and
B
are disjoint;
P
(
A
) =
0
.
30
; and
P
(
B
) = 0
.
55
. Calculate the fol
lowing probabilities.
(a)
P
(
A
or
B
)
.
(b)
P
(
A
c
)
.
(c)
P
(
B
c
)
.
7. You are given the following information:
P
(
A
) = 0
.
65
;
P
(
B
) = 0
.
45
;
P
(
AB
) =
0
.
30
. Calculate
P
(
A
or
B
)
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Chapter 1 Homework Continued
8. Consider a sample space with five mem
bers: 0, 1, 2, 3 and 4. Assume the ELC and
i.i.d. trials. Define
X
=
X
1
+
X
2
, the to
tal of the numbers obtained in the first two
trials. Find the sampling distribution of
X
.
9. Consider a sample space with three mem
bers: 1, 2 and 3. Assume the ELC and i.i.d.
trials.
Define
X
=
X
1
+
X
2
+
X
3
, the total of
the numbers obtained in the first three tri
als. Find the sampling distribution of
X
.
10. Consider a sample space with four mem
bers: 1, 2, 3 and 4. Do not assume the ELC.
Instead assume the following:
P
(1) = 0
.
1
, P
(2) = 0
.
2
, P
(3) = 0
.
3
and
P
(4) = 0
.
4
.
Assume i.i.d. trials. Define
X
=
X
1
+
X
2
,
the total of the numbers obtained in the first
two trials. Find the sampling distribution of
X
.
11. Refer to the previous question. Define
X
=
X
1
+
X
2
+
X
3
, the total of the numbers
obtained in the first three trials.
Find the
sampling distribution of
X
.
12. Refer to the table in problem 10 of the
Chapter 1 Lecture Examples.
(a) Verify (i.e. count 5tuples and then di
vide) my statement that
P
(
X
= 7) =
0
.
00193
.
(b) Verify (i.e. count 5tuples and then
divide) my statement that
P
(
X
=
27) = 0
.
00450
.
(c) Verify the nearly certain interval I
give for
P
(
X
= 17)
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 hanlon
 Mean, Null hypothesis, Probability theory, Statistical hypothesis testing

Click to edit the document details