If {X(t)} is a random process with constant mean u and if XT T 1 | X(t) dt, then {X(t)} is mean-ergodic (or ergodic in the mean), provided 2T -T lim {Var XT} = 0. %3D

Q: What are the right three digits of 3402? Hint. Use Euler's theorem. What is o(1000)?

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Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: Show that Sn is solvable when n ≤ 4.

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Q: - BJ -1]. prove prove A²-A-51 = 0 3 If A =

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Q: prove that div A マ - Kr

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: How many counterexamples are needed to prove that a statement is false?

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Q: he error funct couibnpo 2ha : used in proba a) Show that

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Q: Sy²el+2y®dy

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Q: find fix) and

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Q: Let a, be such that asb. Prove that tx Eqt ax cbx

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Q: beta

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Q: If a is transcedental over Q then a^2 is also transcedental over Q

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: For two real numbers x and y, if 2x + 3y > 7. Prove by contradiction: 18, then either x ≥ 3 or y ≥…

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Q: 1. Prove that fraction where m is z-4

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Q: 1) D Prove that 224 O 210

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Q: w Write down the de finition of IT. 5.

A: Please go through the given definition of Pi given below,

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Q: Prove: If a is a positive even integer and b is an odd integer, then (a,b)=(a/2, b).

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Q: How would I prove this?

A: To prove: The statement

Q: l, tet that 17/2n+3m e integed, prouve iff, 17/9n +5 m and m be

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Q: Prove that du Inlul + C where n= -1 u

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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls

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Q: 2- find aw dw if w = xy + ду +3/1

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