A joint pdf of X and Y is given by f (x, y) = xy² for 0

Q: f X and Y are independent RVs each following N(0, 2), find the pdf of Z = 2X +3Y.

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Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: foz Evaluate the integral: 5x sec (x) dx +C

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Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Formula Used: Volume of the solid generated by the revolving the region bounded by the curve y=f(x)…

Q: The joint PDF of X and Y is given as S2, 0< x< y<1 f(x,y) (0, otherwise

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Q: The joint PDF of X and Y is given as 0<x<y<1 (2, f(x, y) = Q. otherwise

A: Given: f(x,y)=20≤x≤y≤10otherwise

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: The joint pdf of X and Y is f(x, y) = e=Y for 0 <x < y<∞ and zero otherwise. Find the joint pdf of S…

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Q: Suppose X - Exp(B) with density fx(x) = Bexp(-Bx) for x > 0 and B > 0. For Y = X1, where y > 0 is a…

A: From the given information, X~Expβ with density function, fx=βe-βx, x&gt;0 Y=X1γ. 1. PDF of Y:…

Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y g f(x, y, z) 3D…

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Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Please check the region, given region is not bounded, we consider the region bounded by curve, x=0,…

Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

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Q: Suppose that X and Y have joint pdf (8xy 0< y<x<1 f(x, y)=- otherwise Find the joint CDF. Find fy…

A: Given:

Q: Given the function ƒ (x, y, z) = V7y – 3x³ z, calculate the partial derivative with respect to y, in…

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Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

A: Given that The length of rod is π2 and the density of the rod is δ(x)=2-cos(x)  with 0≤x≤π2 To find…

Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: Find the total differential. z = x cos(y) – y cos(x) dz =

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Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: 1. Integrate using Integration by Parts: I sec? x dx

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Q: Assume that X and Y have joint pdf Sr + 3x?y if 0 <r<1 and 0 < y < 1, f(x, y) = %3! otherwise.

A: We know that, Covariance(X,Y) = E(X).E(Y) - E(XY) Here E(X) and E(Y) are given so we'll Calculate…

Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

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Q: sta lis ūcally independent RVs x&y have pdfs fe (x) = 3 (4-x2), - 2<x<2 %3D 32 ノ fy (4) = ニ 1, Find…

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Q: The joint PDF of X and Y is fær(x, y) = {"e * 0sy<x] otherwise .

A: The joint PDF for X and Y is, fx,y=λ2e-λx, 0≤y&lt;x   Given that W=X-Y Let Y=V W+V=X Consider, the…

Q: Evaluate by Gauss divergence theorem for |] 4xz dy dz - y dz dx + yz dx dy S Sin tho a

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Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

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Q: Find an interval where the IVP dy (In t) + y = cot t dt y(2) = 3 has a unique solution.

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Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Let X, Y have the joint pdf {; for x? + y? 0, y > 0 cx fx,y O.W. where c is some constant.

A: Given that,

Q: 2. Given the joint pdf of X and Y, fxx(x, y) = { '0" (4xy 0<x< y <1 other wise Find the marginal…

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Q: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where…

Q: Let X have the pdf 1 p(x) = T(1+ a2)' x E R. %3D Find the pdf of Y = X?.

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Q: The joint PDF of X and Y is 5y -1< x< 1, x² < y<1 fx,y(x, y) = 4 otherwise, %3D Find E(VY).

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Q: What is the formula for the total distance traveled by an object with a velocity v(t) = O - ¹ sin…

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Q: Let y = sin(5x). If Ar = 0.4 at r = 0, use linear approximation to estimate Ay Ay 2 %3D Find the…

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Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: f X,Y(x,y) = 2I(0,y)(x) I(0,1)(y). Solve f

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Q: Given that f(x) has second derivative, f(0) = 0, f'(0) = 1, and the line integral | [xy(x + y) –…

A: Compare the given integrand  with Pdx + Qdy P = xy(x + y) - f(x) Q = f'(x) + x2y

Q: The value of the double integral a x dn dy is 0,

A: To find ∫-aa∫0a2-x2x dx dy : ∫-aa∫0a2-x2x dx…

Q: Find the total differential. z = x cos(y) -y cos(x) dz %3D

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: The joint pdf of two variables X,Y is fxy(x,y)=ae **9) for x20, y20. Find the constant a. Are X and…

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Q: If the joint pdf of (X, Y) is given by fry(x, y) = x + y; 0<x, y< 1, find the pdf of U = XY. ху

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Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the…

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