(a) Find E(XY) (b) Let U = X, V = Y/X. Show that U and V are independent

Q: Find fx, fy, fz. fx = + +2² f(x,y,z) = e¯ (4x²+2y² 12=7 Z

A: f(x,y,z)=e-(4x2+2y2+z2)we know (i)  ∂ ∂x(xn)=nxn-1(ii)  ∂ ∂x(constant)=0

Q: Find the Green's function G" + k²G = 8(x − s), Gʻ(0, s) = 0, G′(0,π) = 0 -

A: To find the Green's function G(x,s) for the given differential equation G′′+k2G=δ(x−s), subject to…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Find r'(t), r''(t), r'(t) · r''(t)

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: Find div F if F(x, y, z) = (x2 + y) i + z2 j + (ey - z) k.           A . 2xy i + k          B. 2x…

A:

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

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

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: If f(x, y) = V + y3, find fy(0, 5).

A:

Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: Let F(x, y, z) y³ 2:5 . What is the value of div F at (1, 2, 3)?

A:

Q: Find y as a function of a if y(0) = 2, y(0) = 3, "(0) = 7. y(x) = y"9y" + 18y = 0,

A: y'''-9y''+18y'=0y(0)=2, y'(0)=3, y''(0)=7To Find: y(x)

Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

A: The gradient is just the vector of partial derivatives. The partial derivatives of f at the point…

Q: Find all values of x and y such that fx(x, y) f(x, y) = x² + 5xy + y² - 15x - (x, y) = ([ = 0 and f…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: -2 In(x) Consider the function f(x, y) 3y

A:

Q: Let X ~ Exp(λ). Find F(X) and E(X).

A: Let X ~ Exp(λ)The probability density function of X is fx(x)=e-λx   ;x>0