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A data dictionary is a table of information about each data element in the system. Initially, in the requirements phase the data dictionary will be the data items from the problem domain. A typical entry will include the name of the item, in which class it is located, the type of the data item, and the semantics of the item.

Fig. 13-5

(32)

The moment generating function and characteristic function are given, respectively, by M(t) (1 t) , ( ) (1 i ) (33)

Fig. 13-6 We apply KCL to the input and output nodes (for convenience, we designate the admittances of the three branches of the circuit by Ya , Yb , and Yc as shown in Fig. 13-6). Thus, Ya 1 3 2 5s=3 5s 6 1 2 Yb 3 5s=2 5s 6 1 s Yc 5 6=s 5s 6

A random variable is said to have the beta distribution, or to be beta distributed, if the density function is xa 1(1 x)b u B(a, b) 0

11

f (x)

(34)

The node equations are I1 V1 Ya V1 V2 Yc Ya Yc V1 Yc V2 I2 V2 Yb V2 V1 Yc Yc V1 Yb Yc V2 By comparing (9) with (12), we get

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Build a data dictionary for the library problem in Example 2.6. Name Author Class Book Type String Object Key Key Object Size < 40 char Semantics Last name, rst name (may be truncated) Abstract concept of the book Key to info about the book Key to patron who made this loan Library s physical copy of a book

where B( , ) is the beta function (see Appendix A). In view of the relation (9), Appendix A, between the beta and gamma functions, the beta distribution can also be defined by the density function

12

f (x)

(a b) xa 1(1 (a) (b) 0

Y11 Ya Yc Y12 Y21 Yc Y22 Yb Yc Substituting Ya , Yb , and Yc in (11) into (13), we nd Y11 s 3 5s 6 s 5s 6 14 13

(35)

A reciprocal network may be modeled by its Pi-equivalent as shown in Fig. 13-6. The three elements of the Pi-equivalent network can be found by reverse solution. We rst nd the Y-parameters of Fig. 13-6. From (10) we have Y11 Ya Yc Y12 Yc Y21 Yc Y22 Yb Yc from which Ya Y11 Y12 Yb Y22 Y12 Yc Y12 Y21 16 [Fig. 13.7 a [Fig. 13-7 b [Fig. 13-7 a [Fig. 13-7 b

where ,

Copy ID ISBN Loan Name Patron Title Copy Book Loan Patron Patron Book Key String Object String Object String Key to physical copy being borrowed 10-20 char International Standard Book Number A borrowing that is still active < 40 char Last name, rst name (may be truncated) Registered holder of library card < 50 char First 50 char of title from title page

are positive. The mean and variance are m a a b , s2 (a ab b)2 (a b 1) (36)

15

1 there is a unique mode at the value xmode a a b 1 2 (37)

Fig. 13-7

Let X1, X2, . . . , Xv be v independent normally distributed random variables with mean zero and variance 1. Consider the random variable x2 where

2 2 X1

The four terminal variables I1 , I2 , V1 , and V2 in a two-port network are related by the two equations (1) or (9). By connecting the two-port circuit to the outside as shown in Fig. 13-1, two additional equations are obtained. The four equations then can determine I1 , I2 , V1 , and V2 without any knowledge of the inside structure of the circuit.

X2 2

CHAP. 13]

A system diagram is a nonformally de ned diagram used to give an overview of a proposed system. It is often used when the more formally de ned diagrams are too limited to express the necessary overview. System diagrams usually incorporate aspects of data ow and use case diagrams. They usually have ovals representing processing parts of the system, data objects representing les and/or databases, boxes representing data, and stick gures representing persons. Arcs are used to show the ow into and out of functions. A challenge with systems diagrams is to maintain consistency in the use of symbols and to give su cient details.

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