Q Let (X, B(R), µ) be a Borel measure space. Suppose that {An = [2n-1, 3n+1]} be a family of elements of B(R). Then u(U"1, ) equals a.0 In=1 b.1 c.3 d.4

Q: Let V=C³ with the standard inner product. Let x=(2,1+i,i) and y=(2-i,2,1+2i). Compute…

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Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: 7. In A ABC,X is the centroid. A A. If CW = 15, find CX and XW. W B B. If BX = 8, find BY and XY. C.…

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Q: Let X N(u, 1) of size n. Obtain UMVUE for u.

A: Given that  Let X  N(μ,1) of size n. Obtain UMVUE for μ

Q: 3. Let SP(la, b, c,d.e) and define W:SXSS as the union function: (A, B)AUB. for ill (A. B) ESXS. (a)…

A: Given: S=P({a, b, c, d, e})Define A:S×S→Ssuch thatA(A, B)=A∪Bfor all (A, B)∈S×S We see that S is a…

Q: Let z=x+iy ∈ C where x∈R\{1}, y∈R, and |z|=1. If w = (z+1)/(z-1), then show that Im(w) = y/(x-1).

A: Use the following formulae, to obtain the required result. Real part of a+ib=aImaginary part of…

Q: Let E = [-2, 3) U {−3, π}. Determine the following max D inf D interior of D boundary of D closure…

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Q: H.W: Let X = {0,1,2, ... ,10} and let A, B be fuzzy sets in X such that %3D A = {x € X is neither…

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Q: (H.W) let X=Rbe amatric space show that the folloowing subset of Rare сотраct or not 1 1 1- E,=|1 -…

A: We have to find the subset is compact or not

Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [2n-1, 3n+1]} be a family of…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that{An = [2n-1 3n+1]]∞ Then µ(U("1, 4n-1])…

A: Borel set means union of sets also an element of that set is also an element of that set, From that…

Q: Q:3 If sequences (xn)&(yn) are both in normed space X and Xn - x & yn →y, then x, + Yn x + y.

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Q: (H.W) let X=Rbe amatric space show that the folloowing subset of Rare сотраct or not 1 1 1- E,=|1 -…

A: As per our guidelines, I solved first three subparts. Kindly request you to repost the remaining…

Q: 8. Let C be the perimeter of the square with vertices at the points z = z = 1+i, and z = i traversed…

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Q: If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2,…

A: From the given information, The provided information are as follows: Zi~i.i.dN0,γ2X1~N0,σ2Zi and X1…

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [Tn-1 12n+1]}, be a family of…

A: Please Check the answer in next step.

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: Y1 Y2 ER3 [Y3. (x, y) : 2x1Y1 + x2Y2 + 5x3Y3, for x = X2 ,y = X3 (a) Show that S = is an orthogonal…

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Q: y Verify Euler's theorem for u = x' In

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Q: 2.2.15. Let X be a metric space, and suppose that xn → I and yn → K. Prove that d(xn, Yn) – + y in…

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Q: 9. Let be a bounded open subset of C, and y: → a holomorphic function. Prove that if there exists a…

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Q: 10. Let X , j= 1,.., n, be i.i.d. r.v.'s such that E(X,)= µ, o'(X)=o', both finite. j' Show that E(X…

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

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Q: metoix space and d[211?(₂) for all ₁2 ER 2,12₂ 17. (*/ 1²(₂) d is matrie X. let (Xid) be d' XXR…

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Q: Let X be a normed space and A € BL(X) be of finite rank. Then σe (A) = σ₁(A) = o(A).

A: 1

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A (A)° = A - int A %3D…

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

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A O (A)° = A – int A %3D…

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

Q: roblem 3 Let (X, M,µ) be a space with measure. Let and A,B E M µ (B)=0. Prove that

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Q: 8. (a) Suppose f : [a, b] → R is integrable and L(ƒ, P) = U(ƒ, P) for some partition P of [a, b].…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Consider Uu=4uzzy u(x,0) = u(x), u₁(x,0) = u₁(x), on the domain -∞<x<∞, 0≤t<∞o. Suppose that both…

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Q: 4. Consider the space (IR,T), where T={R,Ø}u{AcR:[0,1)cA}. If A=(0,1), then the closure of A is:…

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

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Q: 6. The distance between a point x ER and a nonempty set A CR is defined by d(x, A) = inf {\x – y| :…

A: In this question, we have to prove that d(x,A)=0 iff x belong in closer(A)

Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n-1, 12n+1]}, be a family of…

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Q: 1. Consider the following three domains in the space: {(x,y,z) E R³:1 ≤|x+y+z<4}, {(x,y,z) € R³ : 2…

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Q: Let (X, B(R), µ) be a Borel measure space. Suppose that {An = [In-1 12n+1]}, be a family of elements…

A: Given, An=7n-n,12n+1nn=1∞ We need to find the value of μ=Un=1∞n+1n,4n-1nn=1∞

Q: Q5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["+1_ 4n-1 Show that A1 C A2 C…

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

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: Please solve this linear algebra question. Thank you.

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Q: Q5. Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = ["+1, 4n-1]}" be a family of…

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Q: Iw (X, D) discrete space A = {2,3,4s A A Bd(A), Euct CA)? EXercise %3D Fined

A: Given that A=2,3,4 The aim is to find A,A°, Bd(A), Eucd(A) A=2,3,4 And, A°=∅ Here A is closure of A…

Q: IIC sUUset of R". tve R" and let k e R. Prove that S = {x e R":x.v = k} an affine subset of R". %3D

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Q: (a) Suppose ƒ: [a, b] → R is integrable and L(f, P) = U(ƒ, P) for some partition P of [a, b]. What…

A: (a) Given that f:a,b→ℝ is integrable and Lf,P=Uf,P for some partition P of [a, b]. To find: what f…

Q: Theorem [4.1.11] Let A and B be subsets of topological spaces X and Y respectively. Then Int(A × B)…

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Q: Q Let (X, B(R), µ) be a Borel measure space. Suppose that {A, = [7n-1, Then u(U l in-1) equals…

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Q: 3. Determine whether the following sets are open, člosed, both open and closed. Also, decide which…

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Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

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