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1. Why is risk management important Risks can be managed and the e ect of risks can be minimized. However, minimizing risk requires that you identify and manage risks. 2. Consider driving to the airport to catch a plane on an airline that you have not used before. What risks might be unique to this trip to the airport, and which ones might be managed as part of the normal trip to the airport Normal risks Running out of gas, at tires, weather delays, tra c accidents, forgetting suitcases Unique risks Construction on highway to airport, possibly di erent terminal, checkin delays speci c to this airline

It is often convenient to subdivide the area under a density curve by use of ordinates so that the area to the left of the ordinate is some percentage of the total unit area. The values corresponding to such areas are called percentile values, or briefly percentiles. Thus, for example, the area to the left of the ordinate at xa in Fig. 3-2 is a. For instance, the area to the left of x0.10 would be 0.10, or 10%, and x0.10 would be called the 10th percentile (also called the first decile). The median would be the 50th percentile (or fifth decile).

The subscript avg in the average power Pavg is often omitted and so in the remainder of this chapter P will denote average power.

Fig. 3-2

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EXAMPLE 10.4 Find P delivered from a sinusoidal voltage source with Veff 110 V to an impedance of Z 10 j8. Find the power factor. Z 10 j8 12:81 38:78 Ieff V 110 eff 8:59 38:78 A Z 12:81 38:78 W pf cos 38:78 0:78

Just as there are various measures of central tendency besides the mean, there are various measures of dispersion or scatter of a random variable besides the variance or standard deviation. Some of the most common are the following. 1. SEMI-INTERQUARTILE RANGE. If x0.25 and x0.75 represent the 25th and 75th percentile values, the 1 difference x0.75 x0.25 is called the interquartile range and 2 (x0.75 x0.25) is the semi-interquartile range. 2. MEAN DEVIATION. The mean deviation (M.D.) of a random variable X is defined as the expectation of u X m u , i.e., assuming convergence, M.D.(X) M.D.(X) E [u X E [u X mu] mu] a ux

(discrete variable) (continuous variable)

P Veff Ieff cos 110 8:59 cos 38:78 737:43

(61) (62)

1. Analyze the potential risks for the dental o ce problem in 4, Problem 2. Classify the risks as normal or unique to this project.

CHAP. 10]

1. SKEWNESS. Often a distribution is not symmetric about any value but instead has one of its tails longer than the other. If the longer tail occurs to the right, as in Fig. 3-3, the distribution is said to be skewed to the right, while if the longer tail occurs to the left, as in Fig. 3-4, it is said to be skewed to the left. Measures describing this asymmetry are called coefficients of skewness, or briefly skewness. One such measure is given by a3 E[(X s3 m)3] m3 s3 (63)

Then,

The measure s3 will be positive or negative according to whether the distribution is skewed to the right or left, respectively. For a symmetric distribution, s3 0.

Fig. 3-3

If a passive network contains inductors, capacitors, or both, a portion of energy entering it during one cycle is stored and then returned to the source. During the period of energy return, the power is negative. The power involved in this exchange is called reactive or quadrature power. Although the net e ect of reactive power is zero, it degrades the operation of power systems. Reactive power, indicated by Q, is de ned as Q Veff Ieff sin If Z R jX jZj , then sin X=jZj and Q may be expressed by Q Veff Ieff or or Q

Fig. 3-4

9 (10) (11)

Fig. 3-5

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