Steven Weber
Dept. of ECE
Drexel University
ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008)
Recitation 6 Solutions (Friday, May 9)
Answer one of the following two questions. Cross out the question you do not want graded.
Question 1.
A small fishing boat catches
25
fish on a given day. Each fish is of one of two types: sparkly or
plain. A fish is sparkly with probability of
20%
, or plain with probability
80%
. Please do the following:
1.
Using the tables, compute the probability that the number of sparkly fish,
X
, caught by the fishing boat is
between 3 and 7, i.e.,
P
(3
≤
X
≤
7)
.
X
∼
Bin(25
,
0
.
2)
,
P
(3
≤
X
≤
7)
=
P
(
X
≤
7)

P
(
X
≤
3)
=
B
(7
,
25
,
0
.
2)

B
(3
,
25
,
0
.
2)
=
0
.
891

0
.
234 = 0
.
657
(1)
2.
Give the mean and variance for the number of sparkly fish caught by the fishing boat.
E
[
X
] =
np
= 25
×
0
.
20 = 5
,
Var(
X
) =
np
(1

p
) = 25
×
0
.
2
×
0
.
8 = 4
.
(2)
3.
Sparkly fish sell for
$100
while plain fish sell for
$1
. Define the rv
Y
to be the total sale value of the catch
in terms of the rv
X
, the number of sparkly fish.
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 Spring '04
 Eisenstein
 Limit superior and limit inferior, Steven Weber, dmax, dmin x dmax

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