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: 21 - Let V = R3,S = 5 Show that = Span(S) %3D

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Q: f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂ (2) for x = 1, y = 1,2 then x and y are: dependent O…

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Q: W (s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(3, v:(3, – 2) = 7, F.( –…

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Q: then E(y) and V(y) are

A: here given , y =  5x-1  E(x) = 2,  v(x) = 1

Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

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Q: 4. Let u = and v = and w = Compute (u x v) x w. %3D 3

A: u×v=ijk-211103=3i-j-6-1+k0-1=3i+7j-k now find u×v×w u×v×w=ijk37-1-111 =7+1i-j3-1+k3+7 =8i-2j+10k

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0]. %3D

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Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

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A: As per our guidelines we can solve first three subpart and rest can be reposted. Solution-: We find…

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Q: F.T. 3) If X(t) + y(t) = x (2t - 1) =it W+1 Ans: Yow) = [4+jCW+1)]² X(w) and X (w.) = -j(w+1) e 2…

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Q: 43. Let g(u, v) = f(u³ – v³, v³ – u³). Prove that ,2 dg av ди

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Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

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A: We are given: f(x,y)=x2y4 ⇒∂f∂y=x24y3=4x2y3

Q: 10- 13- 16- 19-2 4 12 20 14

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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 f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.O Od.-2 O e. 2

A: For calculating the partial derivative we need to assume one variable as constant and differentiate…

Q: 1 x+R+ 2)²(x+ x+ R+ 4) dx (Hint: Let u= x+R+2 x+R+4

A: ∫1x+R+22x+R+42dx

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A: Since we know that  If x and y are independent the it must satisfy the following condition f(x,y) =…

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: If the equations x = u? - v and y = 2uv define u and v as functions of x and y, find and %3D O A. du…

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Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

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Q: Let f(x,y) = In ( x2+y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 8 O b.7 О с. -2 O d. 3…

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Q: Let f (x) C = C = = x on [0, 5], and let P = {0, c, 5}. Find two values of c in (0, 5) such that Uf…

A: Given function is  f(x)=x The partition P is {0, c, 5} We know that  Uf​(P)=∑i=1n​(Mi​)⋅Δxi​ Where…

Q: 1. Let f(x, y) = x + 2y. Find f (0, 1), f(2, -1), f(a, a), and f(a + h, b) - f(a, b).

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