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Construct an object model for a library. The objects in the simple library shown in Fig. 2.6 consist of the library, books, copies of books, and patrons. None of the methods of the objects are shown. The library has an aggregation relationship with book and with patron. That is, the library is really made up of books and patrons. The relationship between book and copy is neither aggregation nor inheritance. The object book represents the abstraction of a book, while the copy is the physical item that is loaned out. The relationship between patron and copy is called loan. From the view of copy, the role is checked out by and from patron the role is check out. The multiplicities indicate that a copy can either not be checked out or can have this relationship with only one patron at a time ( 0.1 ). The other multiplicity, 0.* , indicates that a patron can have zero or one or many relationships of check out at a time.

48 531,441

Fig. 3-1

1 531,441

CHAP. 3]

72,689 531,441

P(zero 9s)

Starting at the lower left corner of the circuit, for the current direction as shown, we have va v1 vb v2 v3 0 va iR1 vb iR2 iR3 0 va vb i R1 R2 R3

P(one 9)

Fig. 2-6.

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The connection of two or more circuit elements creates a junction called a node. The junction between two elements is called a simple node and no division of current results. The junction of three or more elements is called a principal node, and here current division does take place. Kirchho s current law (KCL) states that the algrebraic sum of the currents at a node is zero. It may be stated alternatively that the sum of the currents entering a node is equal to the sum of the currents leaving that node. The node voltage method of circuit analysis introduced in Section 4.3 is based on equations written at the principal nodes of a network by applying Kirchho s current law. The basis for the law is the conservation of electric charge.

72,689 531,441

4.56. If the probability of a defective bolt is 0.1, find (a) the mean, (b) the standard deviation for the distribution of defective bolts in a total of 400.

EXAMPLE 3.2. Write the KCL equation for the principal node shown in Fig. 3-2. i1 i2 i3 i4 i5 0 i1 i3 i2 i4 i5

(a) Mean (b) Variance np 400(0.1) npq 40, i.e., we can expect 40 bolts to be defective. 36. Hence the standard deviation !36 6.

Fig. 3-2

400(0.l)(0.9)

Since this is positive, the distribution is skewed to the right. (b) Coefficient of kurtosis 3 1 3 6(0.1)(0.9) 36 3.01

Three passive circuit elements in series connection as shown in Fig. 3-3 have the same current i. The voltages across the elements are v1 , v2 , and v3 . The total voltage v is the sum of the individual voltages; v v1 v2 v3 .

Construct an object model for a family-tree system that stores genealogical information about family members. Figure 2-7 indicates that everyone has a birthfamily. Every marriage has a father person and a mother person. Many attributes have been left off the diagram, and no functions are shown.

4.58. The grades on a short quiz in biology were 0, 1, 2, . . . , 10 points, depending on the number answered correctly out of 10 questions. The mean grade was 6.7, and the standard deviation was 1.2. Assuming the grades to be normally distributed, determine (a) the percentage of students scoring 6 points, (b) the maximum grade of the lowest 10% of the class, (c) the minimum grade of the highest 10% of the class.

Fig. 3-3

(a) To apply the normal distribution to discrete data, it is necessary to treat the data as if they were continuous. Thus a score of 6 points is considered as 5.5 to 6.5 points. See Fig. 4-20. 5.5 in standard units 6.5 in standard units (5.5 (6.5 6.7)>1.2 6.7)>1.2 1.0 0.17

If the elements are resistors,

0.17 0) 0)

0.17 and z 0.2738 27%

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