Prove that if 0 < a < y, then ỹ – VI < Vy– a.

Q: Let {X;} be i.i.d.~ Exp(0) and a; > 0. Denote by Z = min{a,X1,..., amX,}. Suppose that 0. Prove that…

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Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express zx andzy in terms of fu , fy , and the…

A: Given, Let z=f(u,Y) u=ax+byY=ax-by

Q: Prove Theorem (A + B )T = AT + B T

A: Prove Theorem (A + B )T = AT + B T

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 I(e) = dr, e> 0.

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Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

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Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: Prove that if Xn X and Ync, then (Xn, Yn) → (X, c).

A: Please see the answer innext step

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 F(x, y,z)=xi + yj+zk, f(x,y,z)=||F(x,y,z)||. Prove that: Vf" = nf"-²F F v(In f) =

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

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Q: Let x, y ∈ R such that x 0.001. Prove that |x · y| = |x| · |y|

A: Given: x, y∈ℝ, x&lt;-0.001 and y&gt;0.001   To prove: x·y=x·y

Q: Prove that if Y:nz+P(x- mz) So thdz

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Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

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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 A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: Suppose that C> 1. Prove that if t > Vm ln C+In C, then ()/F) >C.

A: We will use the following Strining's approximation :  n! ≈ √(2πn) e-n nn To prove the given…

Q: Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and…

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Q: Prove that (aA + bB)t = aAt + bB t  for any A, B belongs to Mm× n(F) and any a, b belongs to F.

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Q: Prove that the function f(x1,x2) = In (e*i+= + eV=i+1) is convex over R².

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Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)

A: In this question we will use basic of vector  calculus i.e gradient of any function and curl of…

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

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Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: Prove that X and Y are independent if and only if R = 0

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Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Let Z ~ N(0,1). Prove for all z 2 0, P(Z > x) S

A: It is an important part of statistics. It is widely used.

Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

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: Let a in F_p, a is non zero then show

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Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

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Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False

A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.

Q: Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x,g (y) = 3y + 4 and h (z) =…

A: Given, Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x, g (y) = 3y + 4 and…

Q: If Z = f(x + g(y)) , prove: Zx * Zyx = Zy * Zxx

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Q: Prove that if X₁X and Ync, then (Xn, Yn) (X, c).

A: For a sequence of random variables X1, X2, X3,... to converge to a random variable X, we must have…

Q: əz Let z = x² + y³, x = 2st and y = s-t². Compute for and ar

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Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: Let u(x) be a solution of u" – q(x)u = 0 with q(x) > 0 such that u(0) and u'(0) are positive. Show…

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Q: Prove that for every y E R, there exists a unique x E R such that 2(x – 1)3 – y = 0. %3D

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Q: Prove that (X+Y) (X+Z) =X+YZ

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Q: 2. Let X ~ U[0, 1] and Yn = X. Prove that Y, 4x.

A: Given that, X~U0,1 Yn=n-1nX

Q: Let x(v, w) = } In(v² + w²). Show that = 0

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

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Q: Prove that S[x] = {a+bx where a,b in R} is subring ℝ[x].

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Q: Prove that if w = f(x,y,z), x=r-s, y=s-t, and z =t-r then ôw ôw ôw + âr' as = 0. ôt

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Q: Prove that if X ⊆ Y then X ∩ Z ⊆ Y ∩ Z.

A: To prove this we will take an element from X∩Z and show that 'a' also belongs to Y∩Z.