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In order for this last quantity to be greater than or equal to zero for every value of c, we must have s2 s2 X Y which is equivalent to r2 1 or 1 r 1. s2 Y X 0 or s2 Y X s2 s2 X Y 1

. complete power triangle for the circuit if the 2.0-

4. Are all relationships between classes speci ed 5. Do all functions have the data necessary for the function to execute 3. Draw a process model for a formal inspection. See Fig. 7-2.

3.43. A random variable X is defined by X 2 3 1 prob. 1>3 prob. 1>2. prob. 1>6 Find (a) E(X ), (b) E(2X e 5), (c) E(X2).

A two-branch parallel circuit, with impedances Z1 4:0 308

3.44. Let X be a random variable defined by the density function f (x) Find (a) E(X), (b) E(3X 2), (c) E(X2). e e 0

3x2 0

and Z2 5:0 608

3.45. The density function of a random variable X is f (x) Find (a) E(X), (b) E(X2), (c) E[(X 1)2].

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, has an applied e ective voltage of 20 V. Obtain the power triangles for the branches and combine them to obtain the total power triangle. Ans: ST 128:1 VA, pf 0:989 lagging Obtain the complex power for the complete circuit of Fig. 10-25 if branch 1 takes 8.0 kvar. Ans: S 8 j12 kVA, pf 0:555 lagging In the circuit of Fig. 10-26, nd Z if ST 3373 Va, pf 0:938 leading, and the 3-

3.46. What is the expected number of points that will come up in 3 successive tosses of a fair die Does your answer seem reasonable Explain. e e 0

Report Assignments Reader Product Give overview Inspect Overview Resolve issues Recorder Results, issues

3.47. A random variable X has the density function f (x)

CHAP. 10]

0 . Find E(e2X>3). 0

Fig. 10-25

3.48. Let X and Y be independent random variables each having density function f (u) Find (a) E(X 3.49. Does (a) E(X Y), (b) E(X2 Y) E(X ) Y2), (c) E(XY ). E(Y), (b) E(XY ) E(X)E(Y), in Problem 3.48 Explain. e 2e 0

3.50. Let X and Y be random variables having joint density function f (x, y) Find (a) E(X), (b) E(Y ), (c) E(X 3.51. Does (a) E(X Y) E(X )

Fig. 10-26 10.34 The parallel circuit in Fig. 10-27 has a total average power of 1500 W. information. Ans: S 1500 j2471 VA, pf 0:519 lagging Obtain the total power-triangle

E(Y), (b) E(XY )

Fig. 10-27

Fig. 7-2.

3.52. Let X and Y be random variables having joint density f (x, y) Find (a) E(X), (b) E(Y ), (c) E(X e 4xy 0 0 x 1, 0 otherwise y 1

Y), (d) E(XY ).

Determine the average power in the 15-

E(X) y)

and 8-

. Find (a) E(X ), (b) E(Y ), (c) E(X2), (d) E(Y2),

Y), (f) E(XY).

Fig. 10-28

3.55. Let X and Y be independent random variables such that X Find (a) E(3X 2Y ), (b) E(2X2 e 1 0 prob. 1>3 prob. 2>3 Y e 2 3 prob. 3>4 prob. 1>4

4. Assuming that the tests are representative of the operational situation, calculate the reliability of a software system that has had 10 errors in 200 test cases. F 1 10=200 0:05 R 1 0:95

, has an applied voltage V 339:4 308 V. Obtain the total apparent power and the overall power factor. Ans: 4291 VA, 0.966 lagging

Y2), (c) E(XY ), (d) E(X2Y ).

3.56. Let X1, X2, . . . , Xn be n random variables which are identically distributed such that Xk c 1 2 1 prob. 1>2 prob. 1>3 prob. 1>6

Obtain the complete power triangle for the following parallel-connected loads: load #1, 5 kW, pf 0:80 lagging; load #2, 4 kVA, 2 kvar (capacitive); load #3, 6 kVA, pf 0:90 lagging. Ans: 14.535 kVA, pf 0:954 lagging

X2 2

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