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ENEE 324
ASSIGNMENT 10
Due Tue 10/13
Problem 10A
An appliance uses one of three circuits (
i
= 1
,
2
,
3). The lifetimes
X
i
(in thousands of hours) of the
three circuits have Gaussian distributions:
X
1
∼ N
(6
.
0
,
(1
.
5)
2
)
,
X
2
∼ N
(6
.
5
,
1
.
5)
2
)
and
X
3
∼ N
(7
.
0
,
(1
.
5)
2
)
(i) (6 pts.)
For each circuit, determine the probability that its lifetime exceeds (
a
) 7,500 hours; (
b
)
8,000 hours. In each case, give an expression in terms of
Q
(
·
) (or Φ(
·
)), as well as the numerical
value.
(ii) (6 pts.)
Suppose the prices of the three circuits are $8.00, $9.00 and $11.00 respectively, and
that the target lifetime is 5,000 hours. If a circuit fails before that, then the appliance is refunded
at $20.00. The expected overall cost to the manufacturer is there
c
i
+ 20
p
i
,
where
c
i
is the circuit cost and
p
i
is the probability that the lifetime is less than 5,000 hours. Which
of the three circuits should the manufacturer use in order to minimize the expected cost?
(iii) (8 pts.)
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This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.
 Fall '05
 Ephrimedes

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