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Statement of Work, version B&RSOW1.0 dated 1/1 XYZ Corporation Coding Standards, version 4.6, dated 7/8/95

Fig. 10-29

(x y)

A single-phase AC source having e ective value 6 kV delivers 100 kW at a power factor 0.8 lagging to two parallel loads. The individual power factors of the loads are pf1 0:7 lagging and pf2 0:1 leading. (a) Find powers P1 and P2 delivered to each load. (b) Find the impedance of each load and their combination. Ans: a P1 97:54 kW, P2 2:46 kW, (b) Z1 0:244 84:26

3.76. Work Problem 3.75 if the joint density function is f (x, y)

3.77. Find (a) Var(X), (b) Var(Y ), (c) sX, (d) sY, (e) sXY, (f) r, for the random variables of Problem 2.56. 3.78. Work Problem 3.77 for the random variables of Problem 2.94. 3.79. Find (a) the covariance, (b) the correlation coefficient of two random variables X and Y if E(X ) E(XY) 10, E(X2) 9, E(Y2) 16. 3.80. The correlation coefficient of two random variables X and Y is covariance.

, Z2 0:043 45:57

2, E(Y )

, Z 0:048 36:87

(x 2y)

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3.1 Organization Project lead (Tom) Development group (Bill, Jane, Fred) SQA group (John) 3.2 Tasks Requirements analysis and speci cation Project planning Cost estimation Architectural design Low-level design Implementation Testing Project monitoring Inspections Reviews Documentation 3.3 Responsibilities Project Lead Tom Responsibilities: Project planning, cost estimation, project monitoring, approvals of all summary reports and plans Requirements Lead Bill Responsibilities: Requirements analysis and speci cation Team members: Jane, Fred Design Jane Responsibilities: Architectural design Implementation Lead Jane Responsibilities: Low-level design and implementation Team members: Fred, Bill Test Lead Bill Responsibilities: All testing and test reports Team members: Fred Documentation Jane Responsibilities: User manual

3.82. Work Problem 3.81 if f (x, y)

A practical voltage source is modeled by an ideal voltage source Vg with an open-circuited e ective value of 320 V in series with an output impedance Zg 50 j100

3.83. Let X and Y have the joint probability function given in Table 2-9, page 71. Find the conditional expectation of (a) Y given X, (b) X given Y. 3.84. Find the conditional variance of (a) Y given X, (b) X given Y for the distribution of Problem 3.81. 3.85. Work Problem 3.84 for the distribution of Problem 3.82. 3.86. Work Problem 3.84 for the distribution of Problem 2.94.

. See Fig. 10-30. a) Find the average power and reactive power delivered by Vg . (b) Find the average power and reactive power absorbed by the load. (c) A reactive element jX is added in parallel to Z . Find the X such that power delivered to Z is maximized. Ans: a Pg 250 W and Qg 200 var, (b) P 200 W and Q 100 var, (c) X 100

3.87. A random variable X has mean 3 and variance 2. Use Chebyshev s inequality to obtain an upper bound for (a) P( u X 3 u 2), (b) P( u X 3 u 1). 3.88. Prove Chebyshev s inequality for a discrete variable X. (Hint: See Problem 3.30.)

1 3.89. A random variable X has the density function f (x) 2 e |x|, ` Chebyshev s inequality to obtain an upper bound on P(u X m u

Fig. 10-30

x `. (a) Find P( u X m u 2). (b) Use 2) and compare with the result in (a).

SQA John Responsibilities: Conduct of all reviews, walk-throughs, and inspections, review of all documents and reports, tracking of all problem reports, and submission of weekly problem report

11.1 INTRODUCTION The instantaneous power delivered from a sinusoidal source to an impedance is p t v t i t Vp Ip cos Vp Ip cos 2!t 1

(a) If we interpret Xk to be the number of heads on the kth toss of a coin, what interpretation can be given to Sn X1 c Xn (b) Show that the law of large numbers in this case reduces to

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