Fix n ≥ 1 and let A be a non-empty closed subset of Rn such that if x, y ∈ A then (x+y)/2∈ A. Show that A is path connected.

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A: Answer

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A: Given: F(x, y) = <x, 0>. C is any path from (a, b) to (c, d).

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

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A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

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A: GivenAc ∪ Bc

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Q: F, there is a disconnection A, B of F such that x E A and y E B. 8.X. If C1, C2 are connected…

A: We use the fact that a set X is connected if there is no continuous function form f from X to Y=…

Q: O Let X,X. X3 beasamPle of size n=3From the Bernolli Pmf Assune Ti ヒ(X、メ,メ) X、+メz+Xg and こ I= X,X t…

A: Using the Neymann factorisation theorem we can find out the sufficient statistic.

Q: If the characteristic function of a RV X is f,(@) and if Y = aX + b, then O,(@) = ibo e

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Q: Prove that any ball (open, closed, half open) in R³ is path connected. or or

A: Please check the answer in next step

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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A: The given theorem is related with the topic product topology. Given that S = π1-1U | U is open in X…

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Q: If S is a subset of T , then u* (T) su* (S).

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Q: If x is a lower bound for S in R then x must be unique..

A: If x is a lower bound for S in R then x must be unique.

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Q: lar, let m = 2 and n e of A and B such that

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Q: 2. Show that the set 3 S = 3 2 2 2 2 spans all of R³ or find an element of R' not belonging to…

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A: Explanation of the answer is as follows

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A: Introduction: Even and odd numbers are distinguished by the following characteristics: Even Number:…

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A: As per our guidelines we are supposed to answer only one question.

Q: Let Á = ry?a, + x³yzay, Evaluate A. dl along the path y = x2 from a(0,0,2) to b(3,9,2) Select one: O…

A: We will find out the required value.

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Q: If S is a subset of T, then u*(T) su* (S)

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Q: Given: mAB = x Prove: mz1 = 180° - x A D Exercises 25, 26

A: Given:           m AB⏜ = x   To prove:              m&lt;1 = 1800 - x

Q: hade in the region(s) that represent the set (AU B)nC' В A

A: Solution of the problem as follows

Q: Show that; is a linearly independent set in R3.

A: S=121,011,201 Let a,b and c be the scalar in R3. Then write the set in term of linear span.…

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A: It is given that, A=ρsinϕ aρ+ρ3 aϕ   According to stokes, theorem (also called Curl theorem),…

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A: The given set is  S=1m,1n  m, n∈N

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A: Introduction: One random variable follows Bernoulli with parameter p and other random variable…

Q: 4. A region D in RN is said to be convex if and only if for every u, v E D and t e (0, 1), then tu +…

A: Given: A region D in ℝN is said to be convex if and only if for every u,v∈D and t∈0,1, tu+1-tv∈D.…

Q: Let X = R, and M = {0}, then span (M) = %3D %3D OR O {0}

A: If, M = {0} then, span(M) = {0}

Q: Find all maps ¢:(Z,+) → (Q*, ×) satisfying O (a + b) = ¢(a) × ¢(b) Va, b e Z

A: We derive the function from the given properties.

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Q: Let fELoi Show that i for any E>o, the set 3- S has a positive measure -

A: For f∈L∞ , f∞=infM&gt;0:μx:fx&gt;M=0For M&gt;0, defining the set AfM=X:1 fx&gt;M⇒For f∈L∞,…

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Q: 2. Write a preference E on R as a subset of R', where a bundle a E Rª is at least as good as a…

A: To write: A preference ⪰ on ℝ+2 as a subset of ℝ+4, where a bundle x∈ℝ+2 is at least as good as a…

Q: Prove that any ball (open or closed or half open) in R³ is path connected.

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Q: Consider a S = {x|x"=1} is S, equals to S?

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