Let X ~ N (0,1) and Y = VX]- The density of Y is given bị

Q: ủ (u x) = 0 for all u, v in R.

A: We will prove whether this is true or false as following.

Q: Question Suppose the r.v. xy, z have a joint prob dersity Function given by; Flzy,z) =L(zty+241)…

A: Suppose the random variable x,y,z have a joint probability function given by; F(x,y,z) =…

Q: Consider the following. f(x, y) = 4x2 − y c = 3, P(2, 13)   Find a unit normal vector to the level…

A:

Q: = f(x,y) = e²+y. For a unit vector u in R?, it is fü(0, 0) = 1. Let z true that

A:

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

A:

Q: Let N be the unit normal to (x,y,z) = R(t). Prove that dN/ds is perpendicular to N.

A:

Q: Prove that c(u × v) = cu × v = u × cv.

A:

Q: Find the Jacobian ∂(x, y) ∂(u, v)for the indicated change of variables. x = 3uv,  y = 2(u − v)

A: on solving this we get the

Q: Let f(x, y) = sih(x) + cas (y), v=0. B. The maximum rate of change of f at P is in the direction v =…

A: Let us solve above problem

Q: Consider the given closed rectangular box with dimensions x cm, v cm and z cm. Assume that x is…

A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

Q: The directional derivative of f(x, y) = x sin y at P.(1, n) in the direction of the vector 31-41

A: We have to find the divergence of the function first.

Q: Find a normal vector to the level curve f (x, y) = c at P.                                    f(x,…

A:

Q: This under subject of Linear Algebra and Vector Analysis

A: Given : z=1-x2-y2             F ⇀ =z-yi^+x -zj^  +x-yk^ Verify : Stokes's Theorem

Q: A normal vector to the tangent plane for the at the point (1, 1, 1) is: y surface x =

A: A(1, 1, 1)z= xyf(x,y,z) =xy-zfx=yfy=xfz=-1Normal vector to the tangent plane for the surface;n^…

Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

A:

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: find laplace of f(x,y,z)=2x3y2z2

A:

Q: 33. Define T: R³ → R³ by y + 2z 2x +3y - z x +2y - 2z x - y a. Find all vectors in R' that are…

A:

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: af Let f(x, y, z) = xy + z². Calculate where x = = s², y = 2st, z = t². მs

A: Step 1: Step 2:

Q: al of the vector î + xj along t

A:

Q: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: Find the flux of F across S, 1.1. S F. N dS where N is the upward unit normal vector to S. F(x, y,…

A:

Q: Find rsint V1+ u+du) dt. dx2 Jo

A: We have to use the formula  Here  We write the second derivative as two derivatives and use f(t)…

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

A: Given: dydx+ycotx=sinx

Q: f(u, v) where u = g(x, y, z), v = ôf Let w = h(z), x = p(t, z) and y = q(t, z). Find

A:

Q: Use triple iutegral in reitanqular coordinates +to tindd te nass of. sphere with den a ensing S こス…

A: mass = density * volumem        = massδ         = densityV        =…

Q: aL d( aL (i = 1,2, ,n) ... aq, dt dg,

A: We have to prove given result:

Q: Let P be the portion of the tilted plane in R' parameterised by r(u, v) = ui + uj + vk where 0 < x <…

A: Given: To explain the correct option of the given statement as follows,