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Find the two elements in a series circuit, given that the current and total voltage are i 10 cos 5000t 23:138 A v 50 cos 5000t 308 V

is the density function for a random variable X. (a) Determine c. (b) Find the distribution function. (c) Graph the density function and the distribution function. (d) Find P(X 1). (e) Find P(2 X 3).

Hence,

2.83. The probability function of a random variable X is given by 2p p 4p 0 x 1 x 2 x 3 otherwise 1).

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Since i lags v (by 53.138), the elements are R and L. The ratio of Vmax to Imax is 50/10. q 50 5000L and tan 53:138 1:33 R2 5000L 2 10 R Solving, R 3:0 , L 0:8 mH.

f (x)

where p is a constant. Find (a) P(0

A series circuit, with R 2:0 and C 200 pF, has a sinusoidal applied voltage with a frequency of 99.47MHz. If the maximum voltage across the capacitance is 24 V, what is the maximum voltage across the series combination

2.84. (a) Prove that for a suitable constant c, F(x) e 0 c(1 x x 0 0 X 2).

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! 2 f 6:25 108 rad=s From Table 9-1, Imax !CVC;max 3:0 A. Then, by the methods of Example 9.2, q q Vmax Imax R2 1=!C 2 6 2 24 2 24:74 V

x )2

is the distribution function for a random variable X, and find this c. (b) Determine P(l 2.85. A random variable X has density function f (x)

The current in a series circuit of R 5 and L 30 mH lags the applied voltage by 808. Determine the source frequency and the impedance Z.

2.86. Two independent random variables, X and Y, have respective density functions f (x) Find (a) c1 and c2, (b) P(X Y e c1e 0

1. Explain why the height example satis es the criteria for valid metrics. 2. A study of grade school children found a high correlation between shoe size and reading ability. Does this mean that shoe size is a good measure of intelligence

Fig. 9-16

g( y)

0 0 l).

Fig. 9-17

1), (d) P(1

At what frequency will the current lead the voltage by 308 in a series circuit with R 8 and C 30 mF

2.87. In Problem 2.86 what is the relationship between the answers to (c), (d), and (e) Justify your answer. 2.88. Let X and Y be random variables having joint density function f (x, y) Find (a) the constant c, (b) P(X function of Y. 2.89. In Problem 2.88 is P(X

1 2, 1 2,

3. Explain why money is a ratio scale measure and not just an interval scale. 4. Explain why GPA is not sound by measurement theory. 5. Why is complexity not readily measurable 6. What is the advantage of having a partial order on the empirical relation system 7. Why is the number of decisions plus 1 an important method for calculating McCabe s cyclomatic number 8. Why is monotonicity an important characteristic of a size or e ort metric such as Halstead s e ort metric

From the impedance diagram, Fig. 9-17, 8 jXC Z Then 308 XC 8 tan 308 4:62 or f 1149 Hz

3 2 ),

A series RC circuit, with R 10 , has an impedance with an angle of 458 at f1 500 Hz. Find the frequency for which the magnitude of the impedance is (a) twice that at f1 , (b) one-half that at f1 .

3 2)

3 2 )

From 10 jXC Z1 458, XC 10 and Z1 14:14 . q 28:28 2 10 2 26:45 (a) For twice the magnitude, 10 jXC 28:28 8 or XC

2.90. In Problem 2.86 find the density function (a) of X2, (b) of X 2.91. Let X and Y have joint density function f (x, y) e 1>y 0

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