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Fig. 9-28 One choice of mesh currents is shown on the circuit diagram, with I3 passing through the 10- resistor in a direction such that Vx I3 10 (V). The matrix equation can be written by inspection: 3 2 32 3 2 7 j3 j5 5 I1 10 08 6 7 4 j5 12 j3 2 j2 54 I2 5 4 5 308 5 I3 5 2 j2 17 j2 0 Solving by determinants, 7 j3 j5 10 08 j5 12 j3 5 308 5 2 j2 0 667:96 169:098 0:435 I3 7 j3 j5 5 1534:5 25:068 j5 12 j3 2 j2 5 2 j2 17 j2 and Vx I3 10 4:35 194:158 V.

xn )

In the netwrok of Fig. 9-29, determine the voltage V which results in a zero current through the 2 j3 impedance.

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Calculate Halstead s basic measures on the factorial code given below: int fact (int n) { if(n == 0 ) { return 1 ; } else { return n * fact (n-1) ; } } operators: int 2; ( ) 3; { } 3; if 1; == 1; return 2; ; 2; else 1; * 1; 1 operands: fact 2; n 4; 0 1; 1 2; basic counts 1 = 10 2 = 4 = 14 2* = 1 N2 = 9 N = 26 N1 = 17 Est N = 10 log2 10 + 4 log2 4 = 10 332 + 4 20 = 332+ 80 = 412 V = 26 log2 14 = 26 38 = 988 V = 3 log2 3 = 3 * 16 = 48 L = 48 / 988 = 0048 9.

xn f(xn)

a xj f(xj)

Fig. 9-29

a x f(x)

CHAP. 9]

where the last summation is taken over all appropriate values of x. As a special case of (2), where the probabilities are all equal, we have E(X) x1 x2 n c xn (3)

Choosing mesh currents as shown on the circuit diagram, 5 j5 30 08 0 1 I2 j5 0 6 0 z 0 V 10 Expanding the numerator determinant by cofactors of the second column, j5 6 V 5 j5 0 0 whence V 35:4 30 08 j5 6 0 10

which is called the arithmetic mean, or simply the mean, of x1, x2, c , xn. If X takes on an infinite number of values x1, x2, c , then E(X) g ` 1 xj f(xj) provided that the infinite sej ries converges absolutely. For a continuous random variable X having density function f(x), the expectation of X is defined as

E(X)

Use the code section from the problem statement to draw the control ow graph and calculate McCabe s cyclomatic number using all three approaches Show which lines of code are represented by which nodes On the CFG, label the regions with Roman numerals and the decisions with lowercase letters See Fig 5-8 E 8, N 6 (or extra nodes might be at the end of the ifs, so E 9 and N 7 or E 10 and N 8 > so C 8 6 2 4 Regions 4 > C 4 Decisions 3 > C 3 1 4.

The network is redrawn in Fig. 9-30 with one end of the 2 j3 impedance as the reference node. By the rule of Section 9.7 the matrix equation is 2 32 3 2 3 1 1 1 1 1 V1 30 08 6 5 j5 2 j3 7 5 j5 76 7 6 5 6 76 7 6 7 6 74 5 4 4 1 1 1 1 1 15 30 08 V 5 V2 5 j5 5 j5 4 6 5 4 For node voltage V1 to be zero, it is necessary that the numerator determinant in the solution for V1 vanish. 30 08 0:200 j0:200 5 0 from which V 35:4 458 V N1 30 08 V 0:617 j0:200 5 4

provided that the integral converges absolutely. The expectation of X is very often called the mean of X and is denoted by mX, or simply m, when the particular random variable is understood. The mean, or expectation, of X gives a single value that acts as a representative or average of the values of X, and for this reason it is often called a measure of central tendency. Other measures are considered on page 83.

Fig. 9-30

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