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Draw a system diagram for a testing tool that instruments a source code, compiles the instrumented code, executes that code with test cases, and then analyzes the results. See Fig. 8-7. Note that the output from the compiler process is another process.

Fig. 4-2

21

values of the t distribution for v degrees of freedom are denoted by tp,v or briefly tp if v is understood. For a tp; for example, table giving such values, see Appendix D. Since the t distribution is symmetrical, t1 p t0.95. t0.5 For the t distribution we have 0 and s2 v v 2 (v 2). (43)

The following theorem is important in later work. Theorem 4-6 Let Y and Z be independent random variables, where Y is normally distributed with mean 0 and variance 1 while Z is chi-square distributed with v degrees of freedom. Then the random variable T Y 2Z>v (44)

where DYY Y11 Y22 Y12 Y21 is the determinant of the coe cients in (9). For the Z-parameters of a two-port circuit to be derived from its Y-parameters, DYY should be nonzero.

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A random variable is said to have the F distribution (named after R. A. Fisher) with v1 and v2 degrees of freedom if its density function is given by

EXAMPLE 13.6 Referring to Example 13.4, nd the Z-parameters of the circuit of Fig. 13-5 from its Y-parameters. The Y-parameters of the circuit were found to be [see (14)] Y11 s 3 5s 6 Y12 Y21 s 5s 6 Y22 s 2 5s 6

f (u)

Fig. 8-7.

v1u)

Substituting into (21), where DYY 1= 5s 6 , we obtain Z11 s 2 Z12 Z21 s Z22 s 3 The Z-parameters in (22) are identical to the Z-parameters of the circuit of Fig. 13-2. The two circuits are equivalent as far as the terminals are concerned. This was by design. Figure 13-2 is the T-equivalent of Fig. 13-5. The equivalence between Fig. 13-2 and Fig. 13-5 may be veri ed directly by applying (6) to the Z-parameters given in (22) to obtain its T-equivalent network. 22

(45)

11.1 The two-phase balanced ac generator of Fig. 11-22 feeds two identical loads. The two voltage sources are 1808 out of phase. Find (a) the line currents, voltages, and their phase angles, and (b) the instantaneous and average powers delivered by the generator.

Percentile values of the F distribution for v1, v2 degrees of freedom are denoted by Fp,v1,v2, or briefly Fp if v1, v2 are understood. For a table giving such values in the case where p 0.95 and p 0.99, see Appendix F. The mean and variance are given, respectively, by m v2 v2 2 (v2 2) and s2 2v2(v1 v2 2 v1(v2 4)(v2 2) 2)2 (v2 4) (46)

The distribution has a unique mode at the value umode a v1 v1 2 ba v2 v2 2 b (v1 2) (47)

CHAP. 11]

Theorem 4-7 Let V1 and V2 be independent random variables that are chi-square distributed with v1 and v2 degrees of freedom, respectively. Then the random variable V V1 >v1 V2 >v2 (48)

Fig. 11-22 Let Z jZj and Ip Vp =jZj. (a) The voltages and currents in phasor domain are VAN Vp 0 VBN Vp 1808 Vp 0 VAB VAN VBN 2Vp 0

t2 1

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