Let X, Y subset U. Suppose that n(X)= 22, n(Y)= 20, and n(X intersect Y)= 16. How many elements are in X’ U Y if n(U)= 40?

Q: If U(x,y)=In(x²-y³) then Ux+Uy= ... XX

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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: Let {u, v} be an orthonormal set in R" and let y = v13 u + 6v. Then, y|| is

A: Here, given that u,v are orthonormal. That is: u·u=1, v·v=1, u·v=v·u=0

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

A: We will use Lehmann-Scheffe theorem to find the uniformly minimum variance unbiased estimator for μ.

Q: Find 3²y of z = In(xy)

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Q: Show that cl S = SU(Bd S) %3D

A: LetS⊆R, claim: closure(S)=S∪Bd S =S ∪ S' by definition bd(S) ={ x∈ℝ/x∉S° & x∉(ℝ-S)°} let  x∈S∪S'…

Q: Let D- Evaluate z dv.

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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 f X,Y (x, y) = (x+y)/21…

A: The joint probability mass function of X and Y is  f(x,y)=(x+y)/21   , x=1,2,3 and y=1,2

Q: Find the fowien senies fon | X), -T<X <A

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Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

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

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Q: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

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Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

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Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

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

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Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

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: Let 9,n be antegers wth 2n and ged (a,n)=1. Show tht of U(Z.) ={a*+nZ:tez} then o#1 mod 6) for all…

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Q: 4. Let xn → 0 and (yn) be bounded. Prove xnYn → 0.

A: Hello, thanks for your question but according to our guidelines I am answering just question number…

Q: Prove: For allintegers aandb, if a|b then a² |b²

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Q: prove: sE121y |Re(z)+| Imcz)l

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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: 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: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

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: 9. For n = 1,..,n, let X, be independent r.v.'s such that %3D P(X,=1)= p,, P(X,=0)=1- p,- Under what…

A: Hello! As you have posted the different questions, we are answering the first question (9). In case…

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: (X), E(Y ) EXY), Cov(X, Y) , σχ, σχ and Py.

A:

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

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

A:

Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – 2, z – x, x – y), then х, х — у), then ||…

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Q: Let x, y, z ∈  ℕ. Suppose gcd(x, y) = 1. Prove that if x | yz, then x | z

A: In the given question we have to prove that if x|yz , then x|z and g.c.d(x,y)=1 and x,y,z∈ℕ. we will…

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: (a) Prove that x, y = -1, y = 1 1 (b) Prove tha and n: m and

A: This is a problem of Number Theory.

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

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Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: Show that lm Casy -1 CoSy-1

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.