Let X = R and Y = {(0, a, 0), a EE R} %3D %3D and V = {(b,0, b), be R} %3D Then X = Y e V %3D O True False

Q: a²f af af and əx' əy :f(x, y) = (x+ y)(2x + y)² Compute se дхду

A:

Q: Find x, y e lº such that || x || ∞ = 1 = || y || = || x+y 2 || x #y.

A: As per the question we have to find two sequences x, y from the norm-space l∞ such that : ||x||∞ = 1…

Q: Evaluate (zy yz + zz)dV [+] B {(z, y, z) | 0< z < 4,0 < y S 10, 0 <z< 4}. %3D

A:

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

Q: 50 W 30 N 40 50 30 20 40 25 60 Part A: AS = Part B: WE = Part C: EN = Part D: AR + RS - AS %3D

A:

Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

A:

Q: Let h(y,z)=y(e)^−z. Calculate ∂h/∂y and ∂h/∂z.

A: Given : hy,z = ye-z

Q: Evaluate 2æz dV where E = {(x, y, 2) | 2 < * < 3, z < y < 2x, 0 < z< z + 2y}

A:

Q: af af and ax 'ay L: f(x.y) = (x + y)(2x + y)² Compute %3D дхду

A: Given that: f(x, y)=(x+y)(2x+y)2

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

A:

Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per…

A: The regression equation is y^=a0+a1x.   Here, y: be the number of medical doctors per 10,000…

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: Let w = x +y+ z, x = u³ + v³, y = eu, z = u – v and u = t+1, v = e*. Find the value of w (0). %3D…

A: Given: To find: The value of w'(0).

Q: Find g(u(x, y), v(x, y)) if g(x, y) = y sin(xy), u(x, y) = x²y', and v(x, y) = Txy. %3D

A: We have given g(x, y)=ysin(x2y), u(x, y)=x2y3 and v(x, y)=πxy. To find gu(x, y), v(x, y), first…

Q: Let W = {a + bX + cX² + dX³; a – b = 0, c = 4b,}. Then the dimension of W is %3D

A:

Q: Evaluate S, y dv with E = {(x, y,z): 0 <x< 3, 0< y < x, (x – y) < z < (x + y)} %3D

A: Use triple integration

Q: Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per…

A: (b) Verify the provided data:

Q: a) Give a condition on two variables X and Y such that E[XY] = E[X]E[Y]. %3D Suppose that X…

A: Given,a) Let, M be random variable which is independent   of X and Y such that , E(M) = 0    Now,…

Q: x+y f(x, y) = 30 for r = 0,1,2, 3; y = 0, 1, 2, %3D nd: P(X s 2, Y = 1); P(X > 2, Y s 1); P(X>Y );…

A: Substituting x=0,1,2,3 and y=0,1,2 in the equation we get values as below.     x=0 x=1 x=2 x=3…

Q: Let D, E ⊂ C be starshaped w.r.t the same z∗ ∈ D ∩ E. Show that D ∪ E, D ∩ E are starshaped

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Q: 2. Wis subset of V- R3 where %3D a W={(x,y;-1) E IR³ | x, y eR}

A:

Q: B. Let Y = {a, b,c} and Z = {1,2} %3D %3D 1. Find Y x Z

A: Given: Y=a,b,c and Z=1,2 To find:  (1) Y×Z (2) Z×Y (3) Y×Y

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: If & = {(z, y, z) | 1< * < 2, z < y < 2a, 0 < z < z +2y} then: SI. 3zz dV ニ

A:

Q: S[(vxvø)•nds, The value of where o(x, y, z) is defined on S is (a) 1. (b) 0. (c) 2x.

A: Concept:

Q: Expand (x − y)(z + w − t)

A: Expand (x − y)(z + w − t)

Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

A:

Q: •√ [F(x, Evaluate f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

A: We need to calculate ∬Sf(x, y, z) dS. Here,  f(x, y, z)=x2+y2+z2S=x+y, x2+y2≤1

Q: Evaluate o -dz where C :|z| = %3D (z-1) (z² – 5z +6) C

A:

Q: Show that if X and Y are independent rv's, then E(XY) = E(X) · E(Y)

A: we have given that, x and y are independent random variables, then, we will prove, E(XY)= E(X).E(Y),

Q: If T = x' - xy+ y', x = pcos 4, y = psin ø %3D Find a) - ôp ƏT b)

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Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

A:

Q: y =c,J,(x) +c_Y, (x) .A y=c,J,(x) +c,Y, (y) .B y=c,,(x)+c_y,(x) .C y=c,J,(y) +c_Yn(x)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: d). Let K = {(x;y) | x,y e R} with operations (x1;y1) (X2;y2) = (x, + x2 + 1; y, +y2 - 2) %3! (ax, +…

A: Given: K=x;y | x, y∈ℝ with operations x1, y1⊕x2, y2=x1+x2+1; y1+y2-2 and a⊗x1;y1=ax1+a-1; ay1-2a+2.…

Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

A:

Q: Let R = Z3[x]and let I = {q(x)(x² + 1)|q(x) E Z3[x]} then I is %3D %3D

A:

Q: Consider X and Y with fx.Y(x, y) in the x = 0 x = 1 table. Specify whether X and Y are independent.…

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)

A:

Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

A:

Q: E (XY)=E (X)E (Y) if x and y are independent. a. b. True False

A: It is given that X and Y are independent variables or events.

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

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.