1.
(
Exercise 1
of
Expected Value
) Let
X
be the sum of the faces obtained by rolling a fair die
twice.
Use the sample space,
S
, to compute
)
7
4
(
≤
≤
X
P
.
Solution.
2
1
36
18
)
1
,
6
(
);
2
,
5
(
);
1
,
5
(
);
3
,
4
(
);
2
,
4
(
);
1
,
4
(
);
4
,
3
(
);
3
,
3
(
);
2
,
3
(
);
1
,
3
(
);
5
,
2
(
);
4
,
2
(
);
3
,
2
(
);
2
,
2
(
);
6
,
1
(
);
5
,
1
(
);
4
,
1
(
);
3
,
1
(
=
=
2.
Let
V
be the product of the faces obtained by rolling a fair die twice.
Use the sample space,
S
,
to compute
)
20
6
(
<
≤
V
P
.
Solution.
36
19
)
3
,
6
(
);
2
,
6
(
);
4
,
5
(
);
3
,
5
(
);
2
,
5
(
);
5
,
4
(
);
4
,
4
(
);
3
,
4
(
);
2
,
4
(
);
6
,
3
(
);
5
,
3
(
);
4
,
3
(
);
3
,
3
(
);
2
,
3
(
);
6
,
2
(
);
5
,
2
(
);
4
,
2
(
);
3
,
2
(
);
6
,
1
(
=
3.
(
Exercise 13
of
Expected Value
) You can invest in either Project A or Project B.
If you invest
in Project A, there is a 30% chance that you
lose
$26,000, a 50% chance that you break even,
and a 20% chance that you make $68,000.
If you invest in Project B, there is a 20% chance that
you
lose
$71,000, a 65% chance that you break even, and a 15% chance that you make $143,000.
Based on the expected value of each, which investment should you make?