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Normal risks Misunderstanding user desires, miscommunication with user, user hardware problems, cost overrun, project delays, and so on Unique risks Interfacing with patient record system 2. Consider a project that has 0.5 percent probability of an undetected fault that would cost the company $100,000 in nes. Calculate the risk exposure. The risk exposure is the sum of the risk exposure for each possibility. 0:005 100,000 0:995 0 $500 3. Consider the use of an additional review for Problem 2 that would cost $100 but eliminate such a fault 50 percent of the time. Calculate this new risk exposure with using the additional review. Is the additional review approach better 0:0025 100,100 0:9975 100 250:25 99:75 $350:00 The additional review approach is better. 4. What would change in Problem 3 if the additional review was only e ective 10 percent of the time The risk exposure would increase. 0:0045 100; 100 0:9955 100 450:45 99:55 550:00 and be marginally worse than the nonadditional review approach. 5. Build a decision tree for the problem in Example 6.3 if in Game A, the payo was $5.00 and if the cost of playing in Game B was $4.00. Should you play either game The risk decision tree is shown in Fig. 6-2. In both games you would expect to lose money. In game A you would lose an average of $0.75, and in Game B you would lose an average of $1.50.

2. KURTOSIS. In some cases a distribution may have its values concentrated near the mean so that the distribution has a large peak as indicated by the solid curve of Fig. 3-5. In other cases the distribution may be

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The unit of reactive power is the volt-amperes reactive (var). The reactive power Q depends on V, I, and the phase angle between them. It is the product of the voltage and that component of the current which is 908 out of phase with the voltage. Q is zero for 08. This occurs for a purely resistive load, when V and I are in phase. When the load is purely reactive, j j 908 and Q attains its maximum magnitude for given V and I. Note that, while P is always nonnegative, Q can assume positive values (for an inductive load where the current lags the voltage) or negative values (for a capacitive load where the current leads the voltage). It is also customary to specify Q by it magnitude and load type. For example, 100-kvar inductive means Q 100 kvar and 100-kvar capacitive indicates Q 100 kvar.

relatively flat as in the dashed curve of Fig. 3-5. Measures of the degree of peakedness of a distribution are called coefficients of kurtosis, or briefly kurtosis. A measure often used is given by a4 E[(X s4 m)4] m4 s4 (64)

EXAMPLE 10.5 and Q. The voltage and current across a load are given by Veff 110 V and Ieff 20 508 A. P 110 20 cos 508 1414 W Q 110 20 sin 508 1685 var Find P

This is usually compared with the normal curve (see 4), which has a coefficient of kurtosis equal to 3. See also Problem 3.41.

Suppose we have a sample space S. If S is discrete, all subsets correspond to events and conversely, but if S is nondiscrete, only special subsets (called measurable) correspond to events. To each event A in the class C of events, we associate a real number P(A). Then P is called a probability function, and P(A) the probability of the event A, if the following axioms are satisfied. Axiom 1 For every event A in the class C, P(A) Axiom 2 For the sure or certain event S in the class C, P(S) P(A1 < A2 < c ) P(A1 < A2) 1 c (2) Axiom 3 For any number of mutually exclusive events A1, A2, c, in the class C, P(A1) P(A2) (3) 0 (1)

are shown as two junctions in (b). However, resistor R4 is bypassed by a short circuit and may be removed for purposes of analysis. Then, in Fig. 2-9(c) the single junction A is shown with its three meeting branches.

In particular, for two mutually exclusive events A1, A2, P(A1) P(A2) (4)

1 heads _

Fig. 2-9

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