Consider X and Y with fx,r(x, y) in the table. Specify whether X and Y are independent. x = 1 x = 2 y = 3 0.2 0.4 (a) Yes (b) No y = 4 0.15 0.25

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A: We wil find the second order partial derivative.

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A: Topic = Algebra

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A: This is a problem of complex analysis.

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A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

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A: Solution

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Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

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Q: 3. Given z =, show that ху xy(zxx + Zyy) уз — х3 2 || x²y2

A: δwδt=δwδxδxδt+δwδyδyδt+δwδzδzδt       =ysin(z2).(-1)+xsin(z2).0+2xyzcos(z2)(2t)

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A: The objective is to prove that

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A: To find the partial derivative.

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A: B). From the given function: z=x2y2x+y And x∂z∂x+y∂z∂y=3z As we know that the Quotient rule:…

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A: X and Y are said to be independent if P(X=x, Y=y) = P(X=x) P(Y=y), for all x,y.

Q: (A) g(z|y) = h(y|x)fy(y)/f=(x) (B) g(r|y) = h(y|x)f=(x)/fy(y) (C) g(r|y) = h(r|y)f=(x)/fy(y)

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

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A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

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Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

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