Steven Weber
Dept. of ECE
Drexel University
ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008)
Recitation 4 Solutions (Friday, April 25)
Question 1.
A computer store purchases
n
computers from the manufacturer at a price of
p
dollars per
computer. The store sells the computers at a price of
q > p
dollars per computer. The manufacturer agrees to buy
back the unsold computers at a price of
r < p
dollars per computer. The number of sold computers is a uniform
random variable, meaning the probability of selling
k
computers is
1
/
(
n
+ 1)
for each
k
= 0
,
1
,
2
, . . . , n
. Please do
the following:
1.
Let
X
be a rv denoting the number of sold computers. Write down a function for the profit (revenue minus
costs) in terms of
X, p, q, r, n
.
h
(
X
) =
qX
+ (
n

X
)
r

np
= (
q

r
)
X

(
p

r
)
n.
(1)
2.
Compute the expected value of the profit. Hint: the sum of the first
n
integers is
n
(
n
+ 1)
/
2
.
E
[
h
(
X
)]
=
E
[(
q

r
)
X

(
p

r
)
n
]
=
(
q

r
)
E
[
X
]

(
p

r
)
n
=
(
q

r
)
n
k
=0
kp
(
k
)

(
p

r
)
n
=
(
q

r
)
1
n
+ 1
n
k
=0
k

(
p

r
)
n
=
(
q

r
)
n
2

(
p

r
)
n
=
n
q
+
r
2

p
.
(2)
www.ece.drexel.edu/faculty/sweber
1
April 25, 2008
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Steven Weber
Dept. of ECE
Drexel University
Question 2.
Let
X
have pmf:
p
(
k
) =
P
(
X
=
k
) =
(1

p
)
p
k
1

p
n
+1
, k
= 0
, . . . , n
(3)
for some positive integer
n
and some
p
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 Spring '04
 Eisenstein
 1917, 1930, Steven Weber

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