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1. Draw an object model for the B&B problem (see Problem 4.3). 2. Draw an object model for the dental o ce problem (see Problem 4.2). 3. Draw a DFD for the B&B system (see Problem 4.3). 4. Draw a DFD for the dental o ce system (see Problem 4.2) 5. Draw a use case diagram for the B&B problem (see Problem 4.3). 6. Draw a use case diagram for the dental o ce problem (see Problem 4.2). 7. Write scenarios for the B&B problem (see Problem 4.3). 8. Write scenarios for the dental o ce problem (see Problem 4.2). 9. Draw a state diagram for the B&B problem as a whole (see Problem 4.3). 10. Draw a state diagram for the data item reservation in the B&B problem (see Problem 4.3). 11. Draw a state diagram for the dental o ce problem (see Problem 4.2). 12. Draw a system diagram for the B&B system (see Problem 4.3). 13. Draw a system diagram for the dental o ce system (see Problem 4.2).

(d) P(not more than 1 tail)

With balanced Y-loads, the neutral conductor carries no current. Even though this system is threewire, the neutralp be added to simplify computation of the line currents. The magnitude of the line may p voltage is VL 2 106:1 150 V. Then the line-to-neutral magnitude is VLN 150= 3 86:6 V. IA VAN 86:6 908 17:32 608 A Z 5 308

It should be mentioned that the notation of random variables can also be used. For example, if we let X be the random variable denoting the number of heads in 3 tosses, (c) can be written P(at least 1 head) P(X 1) P(X 1) P(X 2) P(X 3) 7 8

4.2. Find the probability that in five tosses of a fair die, a 3 will appear (a) twice, (b) at most once, (c) at least two times.

Fig. 11-26

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Let the random variable X be the number of times a 3 appears in five tosses of a fair die. We have Probability of 3 in a single toss Probability of no 3 in a single toss (a) P(3 occurs twice) P(X 2) P(X 5 1 2 5 3 a ba b a b 6 2 6 1) P(X 0) 625 3888 P(X 1) p q 1 6 1 p 5 6

Similarly, IB 17:32 608 A, IC 17:32 1808 A. See the phasor diagram, Fig. 11-27, in which the balanced set of line currents leads the set of line-to-neutral voltages by 308, the negative of the angle of the impedances.

(b) P(3 occurs at most once)

1. What is the advantage of a DFD over other diagrams The data ow through the system and the speci c data that is available to each process are clearly shown. 2. What is the purpose of behavior speci cations and diagrams in requirement speci cations The purpose is to communicate an overview of the proposed system to the user to ensure mutual understanding of the overall behavior of the proposed system.

5 1 0 5 5 a ba b a b 6 0 6 3125 7776 (c) P(3 occurs at least 2 times) P(X P(X 2) 2) P(X 3) P(X 4) 3125 7776

Fig. 11-27

4.3. Find the probability that in a family of 4 children there will be (a) at least 1 boy, (b) at least 1 boy and at least 1 girl. Assume that the probability of a male birth is 1> 2.

A three-phase, three-wire CBA system, with an e ective line voltage 106.1 V, has a balanced connected load with impedances Z 15 308 . Obtain the line and phase currents by the single-line equivalent method.

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