APPM 4/5570
Solutions to Problems from Sections 3.1 and 3.2
10.
a.
{
0
,
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
b.
If we take
S
1
to be the number in use at station 1 and
S
2
to be the number
in use at station 2, then the diFerence random variable de±ned as
S
1

S
2
would take on the values
{
4
,

3
, . . . ,
5
,
6
}
.
c.
{
0
,
1
,
2
,
3
,
4
,
5
,
6
}
d.
{
0
,
1
,
2
}
13.
a.
P
(
X
≤
3) = 0
.
10 + 0
.
15 + 0
.
20 + 0
.
25 = 0
.
70
b.
P
(
X <
3) = 0
.
10 + 0
.
15 + 0
.
20 = 0
.
45
c.
P
(
X
≥
3) = 1

P
(
X <
3) = 1

0
.
45 = 0
.
55
d.
P
(2
≤
X
≤
5) = 0
.
20 + 0
.
25 + 0
.
20 + 0
.
06 = 0
.
71
e.
P
(2
≤
6

X
≤
4) =
P
(

4
≤ 
X
≤ 
2) =
P
(2
≤
X
≤
4) = 0
.
20 + 0
.
25 +
0
.
20 = 0
.
65
f.
P
(6

X
≥
4) =
P
(

X
≥ 
2) =
P
(
X
≤
2) = 0
.
10 + 0
.
15 + 0
.
20 = 0
.
45
(Regarding (e) and (f), it is easier to think about the lines not in use as 6 minus
the number of lines that are in use.)
18.
The maximum values of the two rolls is shown in the box in each case listed
below.
1 is the maximum in 1 out of the 36 cases, 2 is the maximum in 3 out