Given the function fx,r(x,y) ) = {(x² + y²) / 8 [(x² + y²)/8π x² + y²

Q: Let X and Y have the following joint density: S 1, 0<x<1,0 < y < 1, 0, otherwise. fx,y(x, y) = Give…

A:

Q: Is differentiable on (a,b) and F(x) = | f(t) dt , a <x< b, F is continuous on [a.b]. The function d…

A:

Q: Evaluate the line integral f(2x+4y)ds for C: r(t)= ⟨3t2, 4t2+3⟩, 0 =&lt; t =&lt; 2

A: Now, we can compute this integral. We'll need to multiply  (22t2+12)(10t),  integrate with respect…

Q: Consider the one-form y4 W = dæ + (4 ln(10x)y³ + 13y) dy on {(x, y) E R² | x > 0}. If the one-form…

A: Given: The one-form…

Q: Let F(x, y, z) = 6x?i – cos(xy)(i + 5). Calulate the divergence: div F(x, y, z) =

A:

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

A:

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: Compute V · Fand V x F and verify explicitly V - (V x F) = 0. F(x, y, z) = sinh(x – z)i + 2yj+ (z –…

A:

Q: V(x, y, z) = eax cos(2y) sin(6z) where a is a constant. a) b) Find Find a² v dx² a²v дуг : :

A:

Q: Let f EBV (Co,1]). Define F(x) = St Show that F E BV([0,1). [*f(t) dt, x € (0,1], x = 0.

A:

Q: The joint pdf of a two-dimensional RV (X, Y) is given by f(x, y) = xy² + 0Sx 1), P (Y < –),

A:

Q: x + y The joint pdf of X and Y is fxy(x, y) = 3 0 a) Determine E[Y|x=1] b) Determine E[Y|x=0] 0<x<2,…

A: Method: find the marginal and tuen conditional pdf.

Q: Q1. Verify Divergence theorem for the function F = ë,p over the semi-cylindrical volume x? + y? < a…

A: Given the function  F→=e→ρρover the semi cylindrical volume V=x2+y2≤a0≤z≤h, x≥0

Q: Compute the line integral of the scalar function f(x, y) = √√/1 + 9xy over the curve y = x³ for 0 ≤…

A:

Q: Consider an object D bounded by y = 0, y = x², and x = 3 with density p(x, y) = In(y). Compute the…

A:

Q: a) V.VXA-o, b) VX V-D-O マ×(マ×ズ)= マ(アオ)ー ブイ )v(ズx2)=でしマメズ)ーオ(マ×ご) %3D

A:

Q: The joint pdf of X and Y is fXY (x, y) = cx2y, x2 ≤ y ≤ 1 and fXY (x, y) = 0 otherwise. a) Find c.…

A:

Q: Determine k, so that ƒx¸y(x, y) = a) Determine E[Y] kx 0 0<x<y<1 otherwise is a joint pdf.

A: Given function is fX,Y(x,y)={kx      0&lt;x&lt;y&lt;10         otherwise

Q: [kx Determine k, so that fx,y(x, y) = a) Determine fx(0.6) b) Determine fy(0.6) c) Determine…

A: Method: Using the joint pdf to find the margin pdf of x and y

Q: The joint pdf of a two-dimensional RV (X, Y) is given by f(x, y) = xyʻ 8. 0 1), P (Y l¢Y 1), P(X <…

A:

Q: Suppose the density field of a one-dimensional continuum is p = exp[cos(t - x)] and the velocity…

A: The flux of material past x=0 can be computed by integrating the product of the density field and…

Q: Find the mass of a wire in the shape of helix r(t) = cos πt i+sin πt j+8tk 0≤t≤1, where the density…

A: syms x y z r t rho real x=cos(t*pi) y=sin(t*pi) z=8*t  r=[x,y,z] rho=x^2+y^2+z^2…