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Now from Theorem 5-6, page 158, we know that mS2 >s2 and nS2 >s2 are chi-square distributed with m 1 1 2 2 and n 1 degrees of freedom, respectively. Therefore, from Theorem 4-7, page 117, it follows that mS2 >(m 1 nS2 >(n 2 1)s2 1 1)s2 2 S2 >s2 1 1

The I-V equation is V 8I 8:6.

5.27. Two samples of sizes 8 and 10 are drawn from two normally distributed populations having variances 20 and 36, respectively. Find the probability that the variance of the first sample is more than twice the variance of the second.

The number of degrees of freedom for numerator and denominator are n1 m 1 7, n2 n 1 9. Now if S2 is more than twice S2, i.e., S2 2S2, then F 3.70. Referring to the tables in Appendix F, we see that the 1 2 1 2 probability is less than 0.05 but more than 0.01. For exact values we need a more extensive tabulation of the F distribution.

15.6 THEVENIN EQUIVALENT .TF Statement The .TF command provides the transfer function from an input variable to an output variable and produces the resistances seen by the two sources. It can thus generate the Thevenin equivalent of a resistive circuit. The syntax is :TF houtput variablei hinput variablei

Frequency distributions 5.28. In Table 5-4 the weights of 40 male students at State University are recorded to the nearest pound. Construct a frequency distribution.

EXAMPLE 15.10 15-10.

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Table 5-4 138 146 168 146 161 164 158 126 173 145 150 140 138 142 135 132 147 176 147 142 144 136 163 135 150 125 148 119 153 156 149 152 154 140 145 157 144 165 135 128

5,8,5

The largest weight is 176 lb, and the smallest weight is 119 lb, so that the range is 176 If 5 class intervals are used, the class interval size is 57>5 If 20 class intervals are used, the class interval size is 57>20 11 approximately. 3 approximately.

Fig. 15-10 The node numbers and element names are shown on Fig. 15-10. Transfer Function in Fig. 15-10 Vs 1 0 DC 12 E1 4 0 2 0 10 R1 1 2 1k R2 2 0 2k R3 2 3 1k R4 3 4 200 .TF V(3) Vs .END The output le contains the following results: NODE (1) VOLTAGE 12.0000 NODE (2) VOLTAGE 2:0000 NODE (3) VOLTAGE 17:0000 NODE (4) VOLTAGE 20:000 The source le is

One convenient choice for the class interval size is 5 lb. Also, it is convenient to choose the class marks as 120, 125, 130, 135, . . . pounds. Therefore, the class intervals can be taken as 118 122, 123 127, 128 132, . . . . With this choice the class boundaries are 117.5, 122.5, 127.5, . . . , which do not coincide with observed data. The required frequency distribution is shown in Table 5-5. The center column, called a tally, or score, sheet, is used to tabulate the class frequencies from the raw data and is usually omitted in the final presentation of the frequency distribution.

VOLTAGE SOURCE CURRENTS NAME CURRENT Vs 1:400E 02 TOTAL POWER DISSIPATION 1:68E 01 WATTS SMALL-SIGNAL CHARACTERISTICS V(3)/Vs 1:417E 00 INPUT RESISTANCE AT Vs 8:571E 02 OUTPUT RESISTANCE AT V(3) 6:944E 01 Therefore, VTh 1:417 12 17 V and RTh 69:44

Of course, other possible frequency distributions exist. Table 5-6, for example, shows a frequency distribution with only 7 classes, in which the class interval is 9 lb.

Table 5-5

Operational ampli ers may be modeled by high input impedance and high gain voltage-controlled voltage sources. The model may then be used within a net list repeatedly.

Weight (lb) 118 122 123 127 128 132 133 137 138 142 143 147 148 152 153 157 158 162 163 167 168 172 173 177 > >> >> >>>> >>>> > >>>> >>> >>>> >>>> >> >>> > >> TOTAL Tally Frequency 1 2 2 4 6 8 5 4 2 3 1 2 40 Weight (lb)

0,5,6

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