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Z Z TOP x x x has been added to your Cart 1Click ordering is not available for this item Add a gift receipt for easy returns New & Used (16) from $599 FREE Shipping on orders over $2500 shipped by Amazon Other Sellers on Amazon Add to Cart $615 $399 shipping Sold by MovieMarsCDsX˘p Suppose that X ˘P and Y ˘Q We say that X and Y have the same distribution if P(X2A) = Q(Y 2A) for all A In that case we say that Xand Y are equal in distribution and we write X=d Y Lemma 1 X=d Y if and only if F X(t) = F Y(t) for all tSignals and Systems Part 11/ Solutions S313 We see that the system is timeinvariant from T 2T 1x(t T) = T 2y (t T)l = y 2(t T), Tx(t T) = y 2(t T) (b) False Two nonlinear systems in cascade can be linear, as shown in Figure S310

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316 Find the divergence and curl of the following vectors (a) A = e^ ax sin xy ay cos2 xz az (b) B = pz2 cos 4> ap z sin2 az (c) C = r cos 6 ar sin 0 ae 2r2 sin 8 a^ 317 Evaluate V X A and V • V X A if (a) A = x2yax y2zay 2xzaz (b) A = p2zap p \ 3pz\ sin 4> cos (c) A = —— ar — 318 The heat flow vector HWhere g(x;z) is the joint density of Xand Z Di erentiating twice gives g(x;z) = 2 2e (2xz) The marginal of Xis f X(x) = 2 e 2 x and the marginal of Zis f Z(z) = e z so we see that X and Zare independent Problem 6 (p 355 #11) Suppose Xand Yare independent random variables such that X˘Uniform(0;1) and Y ˘Exp(1) CalculateThat is, x y =270 y z =150 w z =100 x w =

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Note 1 Enter the filing date, filing entity, and transmittal number in column C, rows 1, 2, and 3, respectively This information then will be reflected in the 16 RoR ILEC Interstate Rates, 16 RoR ILEC Intrastate Rates, and 16 RoR ILEC Rec Comp Rates worksheets Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeMira mi nuevo video https//ytrocketffmto/celosaknd/youtubeMira mi nuevo álbum #INFINITY https//ytrocketffmto/infinityknd/youtubeEscucha lo nuevo

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X y2 2, (c) 1 y − x y2, (d) −2 The definition of the divergence may be directly extended to vector fields defined in three dimensions, F(x,y,z) = F 1iF 2j F 3k ∇·F(x,y,z) = ∂F 1 ∂x ∂F 2 ∂y ∂F 3 ∂z Exercise 1 Calculate the divergence of the vector fields F(x,y) and G(x,y,z) (click on the green letters for theZ 1 0 f(x)g(x)dx for all pairs of functions f;gin C0;1 Show that this is in fact an inner product, that is, that it satisfies the four properties listed above Proof The first three properties are straightforward to verify using elementary facts about integration (i) hf;gi= Z 1 0 f(x)g(x)dx= Z 1 0ÈD aY >E !É gZ hi h d c i Z W Z a^Z i V i ^ hd b Z ^c iZ a" aZ Xij V a e gd e Z gin >E ^h \ d d Y !

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X =∫y dA I y =∫x dA 2 2 • Evaluation of the integrals is simplified by choosing dΑ to be a thin strip parallel to one of the coordinate axesone of the coordinate axes • For a rectangular area, 2 2 3 h 3 1 0 I x =∫y dA =∫y bdy = bh • The formula for rectangular areas may also be applied to strips parallel to the axes, dI x y dxThe product C = AB is the m×p matrix defined by c ij = r i(A),c j(B)X where r i(A) is the vector in R n consisting of the ith row of A and similarly c j(B) is the vector formed from the jth column of B Other notation for C = AB c ij = n k=1 a ikb kj 1 ≤i ≤m 1 ≤j ≤p Example 212 Let A =} 101 321 and B = 21 30 −11 Then AB =} 12Algebra questions and answers 10 Let A and B be 2by2 matrices and x, y, z be 2vectors such that Ax = By = 1,1, Ay = 1,0, Bx = 0, 1 Determine z when (b) z = (AB)x (c) z (A B)x2 (A B)y (d) z (e) z = (A B)y, (A 3B) (xy)1 (3A B) (x y) Question 10 Let A and B be 2by2 matrices and x, y, z be 2vectors such that Ax

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3 y y ' 2 ' X Y FigureS13 2 Themomentgeneratingfunctionofc 1X 1 c 2X 2 is Eet(c 1X 1c 2X 2)=Eetc 1X 1Eetc 2X 2=(1−β 1c 1t) −α 1(1−β 2c 2t) −α 2 Ifβ 1c 1 =β 2c 2,thenX 1 X 2 isgammawithα=α 1 α 2 andβ=β ic i 3 M(t)=Eexp( n i=1 c iX i)= n i=1 Eexp(tc iX i)= n i=1 M i(c it) 4 ApplyProblem3withc i=1foralliThus M Y(t)= n i=1 M i(t)= n i=1 expλi(et−1Z A p X(x)dx= Z A p(x)dx and p X(x) = p(x) = F0(x) The following are all equivalent X˘P;ax (d) ax 3 Vim, ay 3 V/m, ay 3 V/m, ay 3 V/m, ay 4 V/m, and ö 4 V/m, and ö 3 V/m, and ö 4 V/m, and ö 12 o 1800 450 1350 Figure P79 Plots of the locus of z — O as in Figure the peak is 10 calculatc the in the Using Equation (), we can

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