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Method 1 Completing the construction begun in Problem 14.15, 1 I 0:042 j11:17 10 36:878 18:93 65:138 A a 2 V1 I1 R1 jX11 E1 18:93 65:138 1:2 j0:8 214:4 j0:8 I1 I 238:2 3:628 V Therefore, Zin Method 2 By (14a) of Example 14.5, Zin 1:2 j0:8 22 Method 3 By (14b) of Example 14.5, Zin 1:2 j20 9:6 2 0:3 j5 5:0 36:878 1:2 j20 4:80 j8:94 12:58 61:538 j4:8 0:3 j0:2 5:0 36:878 0:3 j5:0 5:0 36:878 V1 238:2 3:628 12:58 61:518 I1 18:93 65:138

If in Table 5-2 we recorded the relative frequency or percentage rather than the number of students in each class, the result would be a relative, or percentage, frequency distribution. For example, the relative or percentage frequency corresponding to the class 63 65 is 18>100, or 18%. The corresponding histogram is then similar to that in Fig. 5-1 except that the vertical axis is relative frequency instead of frequency. The sum of the rectangular areas is then 1, or 100%. We can consider a relative frequency distribution as a probability distribution in which probabilities are replaced by relative frequencies. Since relative frequencies can be thought of as empirical probabilities (see page 5), relative frequency distributions are known as empirical probability distributions.

114:3 123:258 12:58 61:508 9:082 61:758

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We can represent a frequency distribution as in Table 5-3 by giving each class mark and the corresponding class frequency. The total frequency is n, i.e., c

14.17 In Fig. 14-33, three identical transformers are primary wye-connected and secondary delta-connected. A single load impedance carries current IL 30 08 A. Given

Table 5-3

Since there are f1 numbers equal to x1, f2 numbers equal to x2, . . . , fk numbers equal to xk, the mean is given by x # f1x1 f2x2 n c fk xk a fx n (24)

and N1 10N2 100, nd the primary currents Ia1 , Ib1 , Ic1 . The ampere-turn dot rule is applied to each transformer. N1 Ia1 N2 Ia2 0 N1 Ib1 N2 Ib2 0 N1 Ic1 N2 Ic2 0 or or or 10 10 08 1 08 A 100 10 Ib1 20 08 2 08 A 100 10 Ic1 10 08 1 08 A 100 Ia1

Why does Gunter restrict the terms/events that can be used in a speci cation What is the di erence between a user s requirements and a speci cation Gunter says that a user s requirements must be speci ed in terms/events that are known to the user and may include terms/events hidden to the machine, while a speci cation is designed to be the basis of the implementation and must be speci ed only in terms that are visible both to the machine and the world 3 The proposed system is a face recognition based on image processing The system will have a camera and is intended to prevent nonemployees from entering the company s secret facilities by controlling the lock on the door When a person tries to turn the door handle, the system takes an image and compares it with a set of images of current employees.

Similarly the variance is given by s2 f1(x1 x)2 # f2(x2 x)2 # n c fk(xk x)2 # a f (x n x)2 # (25)

Fig. 14-34

Note the analogy of (24) and (25) with the results (2), page 75, and (13), page 77, if fj >n correspond to empirical probabilities. In the case where class intervals all have equal size c, there are available short methods for computing the mean and variance. These are called coding methods and make use of the transformation from the class mark x to a corresponding integer u given by x a cu (26)

0. The coding formulas for the mean and vari-

14.19 In Problem 14.18, nd the apparent power delivered to the load by transformer action and that supplied by conduction.

where a is an arbitrarily chosen class mark corresponding to u ance are then given by x # s2 a c n a fu a fu2 n a cu #

CHAP. 14]

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