Page 346 - Fundamentals of Probability and Statistics for Engineers

Model Verification 329

:
:
The values of F X [x (i) ] can now be found based on distribution N(30 3, 3 14) for
X. For example, with the aid of Table A.3 for standardized normal random
variable U, we have

27:4 30:3
F X 27:4†ˆ F U p  ˆ F U 1:64†
3:14
ˆ 1 F U 1:64†ˆ 1 0:9495 ˆ 0:0505;

28:7 30:3
F X 28:7†ˆ F U p  ˆ F U 0:90†
3:14
ˆ 1 0:8159 ˆ 0:1841;

and so on.
0
In order to determine d 2 , it is constructive to plot F (x) and F X (x) as
functions of x, as shown in Figure 10.2. It is clearly seen from the figure that
0
the maximum of the differences between F (x) and F X (x) occurs at x ˆ x (4) ˆ
:
29 1. Hence,
0
d 2 ˆjF 29:1† F X 29:1†j ˆ 0:4 0:2483 ˆ 0:1517:
0 05 and n ˆ
With ˆ : 10, Table A.6 gives
c 10; 0:05 ˆ 0:41:

1.0

0.8
0
F (x) F (x)
F X (x) 0.6 X
(x),
F 0 0.4

0.2

0
27 29 31 33
x
0

Figure 10.2 F (x) and F X (x) in Example 10.5.

TLFeBOOK