Statistics 427: Homework #1
Solutions to Assigned Problems
2.3
[8 pts (2,2,2,2) ]
(a)
The sample space for this experiment is
S
=
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
,
(
SFF
)
,
(
FSS
)
,
(
FSF
)
,
(
FFS
)
,
(
FFF
)
}
where
S
denotes success and
F
denotes failure. Event
A
contains all outcomes with exactly two
S
’s:
A
=
{
(
SSF
)
,
(
SFS
)
,
(
FSS
)
}
.
(b)
The event where at least two of the components function contains the outcomes
B
=
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
,
(
FSS
)
}
.
(c)
The system will function if component one functions and at least one of components two and
three functions. So
C
=
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
}
.
(d)
Event
Outcomes
C
0
{
(
SFF
)
,
(
FSS
)
,
(
FSF
)
,
(
FFS
)
,
(
FFF
)
}
A
∪
C
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
,
(
FSS
)
}
A
∩
C
{
(
SSF
)
,
(
SFS
)
}
B
∪
C
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
,
(
FSS
)
}
B
∩
C
{
(
SSS
)
,
(
SSF
)
,
(
SFS
)
}
1