Fundamentals of Probability and Statistics for Engineers

Model Verification 329The values of F X [x (i) ] can now be found based on distribution N(30: 3, 3:14) forX. For example, with the aid of Table A.3 for standardized normal randomvariable U, we have 27:4 30:3F X …27:4† ˆF U p ˆ F U … 1:64†3:14and so on.In order to determine d 2 , it is constructive to plot F 0 (x) and F X (x) asfunctions of x, as shown in Figure 10.2. It is clearly seen from the figure thatthe maximum of the differences between F 0 (x) and F X (x) occurs at x ˆ x (4) ˆ29:1. Hence,With ˆ 0: 05 and n ˆ 10, Table A.6 givesˆ 1 F U …1:64† ˆ1 0:9495 ˆ 0:0505; 28:7 30:3F X …28:7† ˆF U p ˆ F U … 0:90†3:14ˆ 1 0:8159 ˆ 0:1841;d 2 ˆjF 0 …29:1† F X …29:1†j ˆ 0:4 0:2483 ˆ 0:1517:c 10; 0:05 ˆ 0:41:1.00.8F 0 (x), F X (x)0.60.4F 0 (x)F X (x)0.2027 29 31 33Figure 10. 2 F 0 (x) and F X (x) in Example 10.5.xTLFeBOOK