-H.. OProve that fcz) =z²,s coutinuous at z=z, O prove that: if Z#20 is dis continnity at Z=Zo, where 2o

Q: 1. Use an antiderivative to show that for every contour C extending from a point z₁ to a point 22, 1…

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Q: 5) Compute J(x²+y?)dxdy, where D is the intersection of c irc les r=2 cosg and =2sing.

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Q: Let X~ N(u, o2). Let Y = cX+d, where c < 0. Prove that again Y +d²²) just like in Exercise ? 63

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Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Q1) prove the following below i). Corr(X , Y ) ∈ [−, 1, 1] ii) E(X|Y) = E(X) or E(Y|X) = E(Y) ⇒…

A: We need to use the concepts of Variance, Covariance and Expectations to solve given question.

Q: ax? +b?y +c°z?) a'x+ b°y+c°z xyz abc X y Z. if - prove that b %3D 3. a

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Q: Q #2 Let X - R" and ne N and z = 3 X,.G V neN where Gn = { (miy) €R* : y>nuf. gs z a topoligy on X.…

A: Topology means it should satisfy 3 conditions  Empty set and whole set should belong to tau.…

Q: q_2: het R = ZOZ. Showthat the polynomial has infinitely many roots. (1,0) x in R[x]

A: Let R=ℤ⊕ℤ. Show that the polynomial 1, 0x in Rx has infinitely many roots. Definition: The ring ℤ⊕ℤ,…

Q: (b) The For any X1,...X, and Y1,..., Ym, we have: n п т Cov EXi, -ΣΣCον (X, Y) i=1 j=1 i=1_j=1 Hint:…

A: From the property of covariance,  Assume that X and Y are the random variables. Therefore,  CovX,…

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: Aagamant # os Q#os Find he harploce truriJerm og the Jenetim EBinut 26 Ginan that 7(2125) = 7(t)

A: Laplace transform of periodic function: The Laplace transform of a periodic function f(t) of period…

Q: Let X+5x+4. Examine whether the given polynomidl is irreduable over the QUI, ZCXJ, CIX).

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Q: Prove that u exy)= (x+a)Ly+b) is the exact Solution of the pOE Ux Uy = 4xy ucy) where (a) and (b)…

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Q: If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2,…

A: From the given information, The provided information are as follows: Zi~i.i.dN0,γ2X1~N0,σ2Zi and X1…

Q: a) let-1 ≤x≤ 1. Show that b) Using part (a), find En-1/ 1)", cos(x) c) Find The type of singularity…

A: (a)  Let  fx = x2  x ∈ -1, 1          Since fx = x2 is an even function so the Fourier series of fx…

Q: A car moves from points (0, -1,0) and (0,1,0) through a mountain 0.9 that meets the equation. 0.8…

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Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: Let flt.v) = y+3r²e!. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: In r dy If y , then is cosh z

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Q: [n(n+1)]² 2. Prove: Vn e Z*, Ei i=1 2

A: We prove given statement by Mathematical Induction. Mathematical Induction is a mathematical…

Q: 요2s A) for F- 2K1-3y3+ K %3D prove That divc curl È)=0

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Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: Hiw Prove that c=z²,'s coutinuous at z=z. O prove that: if Z#Z0 is dis continnity at Z=Zo, where 2o

A: (1) Calculate the RHL and LHL for the function f(z).…

Q: 2. Show that n n var ΣΧ) ΣΣον(Χ, X ). \i=1 i=1 j=1 Compare this formula with var(X+Y) = var X+var Y…

A: The equation is Var∑i=1nXi=∑i=1n∑j=1ncovXi, Xj.

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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Q: Solfe Linear differential equa bien 1) XY²+ (1+x) Y=e* 2) 5 = 2X + (x + 1)² 27 X+1

A: Since you have posted multiple questions , we will provide the solution only to the first question…

Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

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Q: Which statement is justified by the transitive property of equality? F. (x + y) + z =x+(p +2) G. If…

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Q: 35. Apply the convolution theorem to show that 2e Meu² du = e'erfvi. | (s – 1. (Suggestion:…

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Q: a) For c, a constants, B E R define X = ect+aB, Prove that dX = (c+a?)X;dt +aXpdB. b) For c, a1,...,…

A: We are given a stochastic processes Xt and we have to calculate its total differential dXt . And we…

Q: Which of the following fucntions, f: R→R`, is one-to-one? A. f(x)= x2 O B. f(x)= x2 + 5 В. O C.…

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