Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: fyx if f(x, y) = sin(xy) + x² In y O cos(xy) – xysin(xy) – 4 cos(xy) + xysin(xy) + 2 cos(xy) –…

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Q: If f (x, y) = xcos (xy) then find fæ. cos (xy) – ysin (xy) O cos (y) – xysin (xy) O cos (xy) + xysin…

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Q: If F(x, y, z) = ze +In(y) +y² x

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Q: Find V · (V × F) if F(x, y, z) = sin xi + cos(x – 2y)j + 8zk. | V ·(V × F) :

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Q: calculate r'(t) and T(t), and evaluate T(1). r(t) =〈cos πt,sin πt,t〉

A: Given :                   r(t) = cos πt , sin πt , tDifferentiating with respect to t, we get…

Q: h(t) = / e -3(t-T) cos(27)dr. This is the convolution of two functions f(t) and Consider g(t). That…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Is FdR path independent? Explain briefly. C₁

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Q: Let f(x, y) be a differentiable function of 2 variables and let r(t) = 3 sin(t)i + 3 cos(t)j. If…

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Q: Consider f(x, y) = (2x² + xy + 1, xy, x² + y²) and let c = (1,-1). Find Df(c) by definition.

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Q: 3) Is the function y(t)=cos(x(t)) linear or not?

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Q: If f(x,y,z) = 2x² − yz + xz², where x = 2 sint, y = t² − t + 1, and z = e−³t, find f't)

A: from chain rule of derivaties…

Q: Let f(y) be the function such that S f(y)dy=y In (4 + 9y²) + C. 1 Evaluate f 4x f(x² + 1)dx.

A: Calculation of Required Value.

Q: Let f(x, y, z)= exy sin(x+y) Calculate fxxz· z²+1

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Q: Let h(x, y) = x5 + y sin²x x² + y² 0, { 25 if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: Let f(x) = cosx²) and g(x) = vx. The (natural) domain of (f • g)(x) is = Cos

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Q: 2 Iƒ ƒn(x) = efn−1(x) for all ne N and fo If d nd {ƒn(x)}. dx

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Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) 7. Find r'(1) %3D…

A: Recall: The derivative of a composition is the product of the derivative of the outer function (…

Q: Let f(x, y) = x° – 3xy. - fa(x, y) = %3| fy(x, y) = f-(1, 3) = fy(1, 3) %3D

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Q: Find a harmonic conjugate v(x, y) of u(x, y) = e e sonding analytic function ƒ(z) = u(x, y)|+ iv(x,…

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Q: Let u(x, y) = e¹ cos y + xy. Show that u(x, y) is harmonic. Find an analytic function g(z) such that…

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Q: 5. Let f(x, y) = sin(2.xy). Find f.(x,y) A) f,(x,y)= 2xcos(xy) B) f,(x,y) = 2y cos(xy) C) f.(x,y)= 2…

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Q: Compute the dz in the function z = ety sin (xy) A. dz = ze"(cos (zy) + sin (ry) dz+ ye"lcos (ry) +…

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Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), e" + cos(V)). Use…

A: gu(0,0) = (6, 6) gv(0,0) = (4, 0).Explanation:We can calculate gu(0,0) and gv(0,0) using the partial…

Q: y3 be a harm C conjugate. D[ is equal to

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Q: Let U (x, y) = e-(y sin x Find a real-valued function V (x, y) such that f(z) = U + iV is analytic.…

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