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Write scenarios for the simplified vi editor using each use case in Example 8.4. Use semicolons to separate actions. Use parentheses to contain comments or conditions. Create le vi lename ( le does not already exist) Open le vi lename ( le already exists) Insert text I ; <desired text> ; <esc> i ; <desired text> ; <esc> O ; <desired text> ; <esc> o ; <desired text> ; <esc> A ; <desired text> ; <esc> a ; <desired text> ; <esc> Modify text cw ; <new text> ; <esc> dw dd x Save le ZZ Note: Not all sequences are shown. For the sake of brevity, not all operations are shown. In an actual specification, efforts should be made to show all operations and significant sequences of operations. In this example, each scenario represents only a part of the use. Alternatively, each scenario could run from open file to close file.

Suppose that A1, A2, c, An are mutually exclusive events whose union is the sample space S, i.e., one of the events must occur. Then if A is any event, we have the following important theorem: Theorem 1-11 (Bayes Rule): P(Ak u A) P(Ak) P(A u Ak)

CHAP. 11]

(24)

Fig. 11-16

a P(Aj) P(A u Aj)

This enables us to find the probabilities of the various events A1, A2, c, An that can cause A to occur. For this reason Bayes theorem is often referred to as a theorem on the probability of causes.

Three-Wire Without the neutral conductor, the Y-connected impedances will have voltages which vary considerably from the line-to-neutral magnitude.

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In many cases the number of sample points in a sample space is not very large, and so direct enumeration or counting of sample points needed to obtain probabilities is not difficult. However, problems arise where direct counting becomes a practical impossibility. In such cases use is made of combinatorial analysis, which could also be called a sophisticated way of counting.

The details of state diagrams were covered in 2. When being used as part of the requirements speci cation, it is important that the states re ect domain conditions that are understandable to the users. States that are only signi cant to the implementation should be coalesced into domain signi cant states. Additionally, the allowed transitions must include all allowed transitions from the scenarios. Sequences that are not intended in the proposed system should

EXAMPLE 11.7 Figure 11-17(a) shows the same system as treated in Example 11.6 except that the neutral wire is no longer present. Obtain the line currents and nd the displacement neutral voltage, VON .

If a fair die is to be tossed 12 times, the probability of getting 1, 2, 3, 4, 5 and 6 points exactly twice 12! 1 2 1 2 1 2 1 2 1 2 1 2 a b a b a b a b a b a b 2!2!2!2!2!2! 6 6 6 6 6 6 1925 559,872

The expected number of times that A1, A2, . . . , Ak will occur in n trials are np1, np2, . . . , npk respectively, i.e.,

Fig. 11-17 The circuit is redrawn in Fig. 11-17(b) so as to suggest a single node-voltage equation with VOB as the unknown. VOB VAB VOB VOB VBC 0 ZA ZB ZC 1 1 1 150 2408 150 08 VOB 6 08 6 308 5 458 6 08 5 458 from which VOB 66:76 152:858 V. Then, IB VOB 11:13 2:858 A ZB

E(X1)

Point O is displaced from the neutral N by a phasor voltage VON , given by 150 VON VOA VAN 100:7 81:088 p 908 20:24 39:538 V 3 The phasor diagram, Fig. 11-18, shows the shift of point O from the centroid of the equilateral triangle. See Problem 11-13 for an alternate method.

np1,

E(X2)

Fig. 11-18

not be allowed in the state diagram. This may be di cult, since the existence of a transition in a scenario does not prohibit other transitions. The following are rules for using state diagrams in requirement speci cations: 1. All states must be domain signi cant. 2. All sequences from scenarios must be allowed. 3. All prohibited scenarios must not be allowed.

np2,

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