Fundamentals of Probability and Statistics for Engineers

The values of FX[x(i)
X. For example, with the aid of Table A.3 for standardized normal random
variable U, we have

and so on.
In order to determine d 2 , it is constructive to plot F^0 (x) and FX(x) as
functions of x, as shown in Figure 10.2. It is clearly seen from the figure that
the maximum of the differences between F^0 (x) and FX(x) occurs at x x(4)

With 0 05 and n 10, Table A.6 gives

F^0 (x) F

X(x)

1.0

0.8

0.6

0.4

0.2

0

27 29 31 33

x

(^0) F
(x
),
FX
(x
)
Figure 10. 2^0 F(x) and FX (x) in Example 10.5.
Model Verification 329
] cannowbefoundbased on distribution N(30 3, 3 14) for::

FX… 27 : 4 †ˆFU

27 : 4  30 : 3



3 : 14

p



ˆFU… 1 : 64 †

ˆ 1 FU… 1 : 64 †ˆ 1  0 : 9495 ˆ 0 : 0505 ;

FX… 28 : 7 †ˆFU

28 : 7  30 : 3



3 : 14

p



ˆFU… 0 : 90 †

ˆ 1  0 : 8159 ˆ 0 : 1841 ;

ˆˆ

d 2 ˆjF^0 … 29 : 1 †FX… 29 : 1 †jˆ 0 : 4  0 : 2483 ˆ 0 : 1517 :

ˆ : ˆ

c 10 ; 0 : 05 ˆ 0 : 41 :

29 1. H ence,: