Let a and b be any real numbers. Prove that Cov (ax, by) = abCov (x, y).

Q: Let J={a: aER}, then I is Borel algebra.

A: False Statement' Detailed Explanation

Q: Prove that Cov (x, y) = E (xy) – E (x) E (y).

A: Cov(x,y) is covariance of x and y. E(x) is expected value of x E(y) is expected value of y.

Q: Prove that (C, +) ≈ (R × R, +).

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Q: Let A={x e R|-1sx s1} = B, Show that f:A →B given by f (x)=x|x| is a bijecti on.

A: we have to show that given function is bijective

Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let r = ri+ yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let A E Mnxn(R), show that it is possible to express A as the product, A = PQ where P,Q € Mnxn(R),…

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Q: Prove that V = Vw+ Vg; that is, E(X x - X )²= £ (x – X,)²+ £(x,. – X)? jk j,k j,k j,k

A: The solution

Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: let theorem a, bor about a) Find such that acb. Use the axioms and that : prove R to b) Find CEIN:…

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Q: alue of the pur C: |z| = (:-1)(z-

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Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

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

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Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

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Q: Prove that c = cn. i=1

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Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: Let j = 7 and U=span(ü), with ü = -6. Write j = ã1+ã2, where 1 in U and az in U-.

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: find the values of c that satisfy Rolle's Theorem

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Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: Let A, Be Mnxn (F). (a) Prove that if A~ B, then At ~ Bt.

A: From the given information. The matrices A and B belong to M of order nxn. It is required to prove .

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p&gt;1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x&lt;0 when…

Q: Let A, Be M, (C) be positive definite. Prove that (4+ B)" s(A" +B").

A: Let A,B∈Mnℂ be positibve definite.  To prove A+B-1≤14A-1+B-1 Since, A and B are positive definite,…

Q: 2. (– 13 + 3i)31

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: U prove that In (l+x)) 2.

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Q: Prove that, IXI<a Rf and If -aL X Z a

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Q: Prove that tr(aA + bB) =a tr(A) + btr(B) for any A, BE M11 xn(F).

A: Prove that traA+bB=a trA+b trB for any A,B∈Mn×nF

Q: Prove that for all values of the constant A, eAInt = e In.

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Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: How to solve this?

A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…

Q: Prove that if A ϵ Mnxn(F) has two identical columns, then det(A) = 0.

A: Given: A∈Mn×nF i.e. A is a matrix of order n×n.   Consider a matrix with first two column as…

Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: Express −i+j in the form [a,b]

A: Simplification

Q: Show that the functions x and x2 are orthogonal in P5 with inner product defined by (5), where xi =…

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Q: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If Cov(x,y) = 0, then X and Y are uncorrelated Select one: O True False

A: If two variables are independent then their covariance is zero and we, say that they are…

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: dv Prove that 4u/2n

A: We use Gamma function to prove the given result.

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

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Q: Suppose f" exists and is bounded on Co,0), Prove that if bam fa)=0, then bim fGx)=0.

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Q: Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A: Given that, f1(x)= x, f2(x) =cos2x and interval is [0, 90o] Wehave to find that the functions are…

Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: Which theorem can be used to prove that ΔROM ΔΡΜΟ M P.

A: We can answer the question as below

Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)