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Fig. 14-28 The voltage across the j5 is partly conductive, from the currents I1 and I2 , and partly mutual, from current I1 in the 4 reactance. V I1 I2 j5 I1 j3 29:27 49:728 V Of course, the same voltage must exist across the capacitor: V I2 j8 29:27 49:728 V

(13)

Instead of taking differences of statistics, we sometimes are interested in the sum of statistics. In that case the sampling distribution of the sum of statistics S1 and S2 has mean and standard deviation given by mS1

14.13 Obtain Thevenin and Norton equivalent circuits at terminals ab for the coupled circuit shown in Fig. 14-29.

(14)

In open circuit, a single clockwise loop current I is driven by the voltage source. I 10 08 1:17 20:568 A 8 j3

If X1, X2, . . . , Xn denote the random variables for a random sample of size n, then the random variable giving the variance of the sample or the sample variance is defined in analogy with (14), page 77, by S2 (X1 # X)2 (X2 # X)2 n c (Xn # X)2 (15)

H. Dharma, Quantitative Models of Cohesion and Coupling in Software, Journal of Systems and Software, 29:4, April 1995.

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# Now in Theorem 5-1 we found that E(X) m, and it would be nice if we could also have E(S2) s2. Whenever the expected value of a statistic is equal to the corresponding population parameter, we call the statistic an unbiased estimator, and the value an unbiased estimate, of this parameter. It turns out, however (see Problem 5.20), that E(S2) which is very nearly

Fig. 14-29 Then V 0 I j5 4 I j6 4:82 34:608 V. To nd the short-circuit current I 0 , two clockwise mesh currents are assumed, with I2 I 0 . 8 j3 10 4 j1 0 0:559 83:398 A I0 8 j3 4 j1 4 j1 7 j5 V0 4:82 34:608 8:62 48:798 I0 0:559 83:398

(16)

Z0

30). The desired unbiased estimator is defined by # X)2 n 1 c (Xn # X)2 (17) (18)

# X)2

The equivalent circuits are pictured in Fig. 14-30.

E(S2)

14.14 Obtain a conductively coupled equivalent circuit for the magnetically coupled circuit shown in Fig. 14-31.

Tom and Sue are starting a bed-and-breakfast in a small New England town. [1] They will have three bedrooms for guests. [2] They want a system to manage the [2.1] reservations and to monitor [2.2] expenses and profits. When a potential customer calls for a [3] reservation, they will check the [4] calendar, and if there is a [5] vacancy, they will enter [6.1] the customer name, [6.2] address, [6.3] phone number, [6.4] dates, [6.5] agreed upon price, [6.6] credit card number, and [6.7] room number(s). Reservations must be [7] guaranteed by [7.1] 1 day s payment. Reservations will be held without guarantee for an [7.2] agreed upon time. If not guaranteed by that date, the reservation will be [7.3] dropped. Design: Class [A] B&B attributes: [A.1] day* daylist[DAYMAX]; [A.2] reservation* reslist[MAX]; [A.3] transaction* translist[TRANSMAX] methods: [A.4] display calendar by week [A.5] display reservations by customer [A.6] display calendar by month Class [B] day attributes: [B.1] date thisdate [B.2] reservation* rooms[NUMBEROFROOMS] methods:[B.3] create(), [B.4] addreservation(), [B.5] deletereservation() Class [C] reservation attributes: [C.1]string name [C.2] string address [C.3] string creditcardnumber [C.4] date arrival [C.5] date guaranteeby [C.6] int numberofdays [C.7]int roomnumber methods: [C.8] create() [C.9] guarantee() [C.10] delete() Class [D] transaction attributes: [D.1] string name [D.2] date postingdate [D.3] oat amount [D.4] string comments

Because of this, some statisticians choose to define the sample variance by S2 rather than S 2 and they simply replace n by n 1 in the denominator of (15). We shall, however, continue to define the sample variance by (15) because by doing this, many later results are simplified.

Referring to Example 5.5, page 155, the sample variance has the value (4 6)2 (7 6)2 (5 5 6)2 (8 6)2 (6 6)2

(4a)

while an unbiased estimate is given by 5 2 s 4 (4 6)2 (7 6)2 (5 4 6)2 (8 6)2 (6 6)2

Fig. 12-13

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