1. Assume Y=1+X+u, where X, Y, and u=v+Xare r.v.S, v is independent ofX; E(v)=0, Var(v)=1, ECX) 1, and Var(X) 2 1) Calculate E(uX=1), E(Y]X=1), E(u|X=2), E(Y]X=2}, E(uX), ECY]X), E(u) and E(Y) 2) Calculate Var(u|X=1), Var(Y\X=1), Var(u|X=2), Var(Y]X=2), Var(u|X), VarYX),

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: 6. Consider the PDE u; +u ux - u Uy = 0 for - ∞<x< ∞, - ∞<y< ∞, and 0 <t< ∞ with u (0, x, y) = (x -…

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Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

Q: Suppose that w = f(r, s, t), where r = r(x, y), s = s(r, y), and t = t(x, y). Which of the following…

A: Solution is given below:

Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

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Q: et T E L(V,W), and U e L(W, X). Prove that UT : V → X is also linear

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Q: If u = f(y — z, z — x, x — y), then ux +uy + uz =

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Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

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Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: dik koordinatylarda x,y öyleki x kare artı y kare küçüktür beş denkleminin grafiğini çiziniz

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Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…

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Q: - (19,8) (10,0) (19,8) ) Show that So fdx + gdy = Sao.0 24x?y dx + 24y2x*dy is independent of path:…

A: Let's find.

Q: If U(x,y)=In(x²-y³) then U+Uy= . O (2x+2y)/ x^2+y^2 O (2x-2y)/ x^2+y^2 O (2x-xy)/ x^2+y^2

A: Let's find.

Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

A: We have to choose the correct answer from the given options according to the given condition

Q: If U(x,y)=In(x²-y²) then Ux+Uyy= XX .....

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Q: Part 1 and 2

A: 1)Given DataY= 1+X+uu = v + XE(v) = 0Var(v) = 1E(X) =1Var(x) =21)E(u|X = 1)E(u|X = 1) = E(v+X| X=1)…

Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: O a. If F(X,Y)=F(X)F(Y), it is not necessarily true that p(XY)=p(X)p(Y) O b. If p(XY)=p(X)p(Y), then…

A: Given the statement(s) : We need to choose the correct statement(s).

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

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Q: 13. Let f(x, y, z) = xy+z², with x(s,t) = s², y(s, t) = 2st, and z(s, af/ds and df/dt %3D %3D

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Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: 3. If Rw (T) is the autocorrelation of a white noise w(t) and S e-217| Rw(t)dt = 1, find Sw(f).

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Q: Example 3.8. Forx = 1,2,3 and y = 1, 2, let the joint pmf of X and Y be defined by I+y fx,y(r, y) =…

A: XY X=1 X=2 X=3 Total Y=1 2/21 3/21 4/21 9/21 Y=2 3/21 4/21 5/21 12/21 Total 5/21 7/21 9/21 1

Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False

A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.

Q: Suppose that w = f(x, y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: By using the chain rule for partial differentiation we will find the value of it.

Q: 1) Aşağıdaki u(x, y) fonksiyonu harmonik midir? Neden? Cevap olumlu ise f(z) = u(x, y) + iv(x, y)…

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Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: If U(x,y)=In(x²-y) then Ux+Uyy= O (2x+2y)/ x^2+y^2 O (2x-2y)/ x^2+y^2 O (2x-xy)/ x^2+y^2

A: Uxx+ Uyy of the function U

Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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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: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn…

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Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: 5. Consider the PDE u: +ux - uuy = 0 for - o<x< ∞, - 0<y< ∞, and 0 <t< c with u (0, x, y) = - y.…

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Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: 1) Let s,T: e defined by Sx = (0,x1, X2, - ) Tx - (x2,X3, Xyy ..) .. Show that (i) Ilsil = TII = 1.…

A: