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1
Lecture of September 21
Lecture of September 21
•F
r
o
m
L
a
s
t
C
l
a
s
s
 Normal distribution
 Standardized normal variable and
Φ
(
⋅
)
 Two important results
• HW#3 due in class on 09/26.
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Three shafts are made and assembled in a linkage. The length of each shaft,
in centimeters, is distributed as follows:
Shaft 1:
x
1
~
N
(75, 0.09)
Shaft 2:
x
2
~
N
(60, 0.16)
Shaft 3:
x
3
~
N
(25, 0.25)
(a) What is the distribution of the linkage length
L
?
Example 2.7
Example 2.7
1
2
3
x
1
x
2
x
3
L
variance
σ
2
3
(b) What is the probability that the linkage will
be longer than
160.5 cm?
Example 2.7 (continued)
Example 2.7 (continued)
1
2
3
x
1
x
2
x
3
L
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• If
(1)
(2)
x
1
,
x
2
, …,
x
n
are normally and independently distributed,
(3)
x
i
~
N
(0, 1), i.e., all
x
i
's are standard normal
Then,
y
follows a
(chisquare) distribution
Chi
Chi
–
–
Square Distribution
Square Distribution
(with degrees of freedom
(with degrees of freedom
n
n
)
)
2
2
2
2
1
n
x
x
x
y
+
+
+
=
L
2
n
χ
• The subscript "
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This note was uploaded on 02/14/2011 for the course ISEN 314 taught by Professor M during the Fall '10 term at Texas A&M.
 Fall '10
 M

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