The property S (2, y) drdy = S Saf (x, y) dydx is true according to the theorem of O None of these O Cassini O Fubini O Lubini

Q: let fERiema nn Tabland f(X)zo fok XE [aib] then Riemanninteral x 9.

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Q: 5) Proof that: var (3₂)ARI when p= 0 = ß₂ Exy Σ.χ2

A: To prove thatwhen (i.e., when the autocorrelation coefficient is zero), let's consider the…

Q: Q1) prove the following below i). Corr(X , Y ) ∈ [−, 1, 1] ii) E(X|Y) = E(X) or E(Y|X) = E(Y) ⇒…

A: We need to use the concepts of Variance, Covariance and Expectations to solve given question.

Q: 3{x.y.2) : x+y²+z's 1024, z2 o}. Let D= Evaluate z dv.

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Q: Evaluate (2z + z – i) dz J|z-il=1

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Q: 4) Evaluate ĺ jedydx 29f071p =

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Q: p[rz 23] If X is a N(2,3), find PY2 where Y+1-X.

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Q: Solve y' = y'x.

A: solve y'=y2x3

Q: If z = 3x2 – 2y3, x = 1+ s²t and y = 33 – t2, then dz %3D O a) 6x(1+ s²)+ 12ty O b) 6s²x – 12ty - c)…

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Q: 5. Let f: NxN → Z be defined by f(m, n) = your answers. What is the preimage of 0? =m-n. Is f…

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Q: 5. Let U ~ U[5, 10] and let X = I5,7) (U) be the indicator function of [5, 7) and let X,…

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Q: Write the following expression in terms of sine and cosine, and simplify it. (The final expression…

A: We use Trigonometry identities

Q: S. Which of the fliowing is te gerl lutin to difiential gu e (a) e+ (b) y (e) yeeoo (4) None of the…

A: Consider the provided question, Given D.E,  y''-4y'+8y=0 We need to find the general solution of the…

Q: dz; |z – i| = 1 (z – i)3

A: We have to use the Cauchy integral formula to evaluate the following integral ∮ ez2z-ι3dz over the…

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: S 289 xe

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Q: 13. Let T, O E L(V, W). Show that rk(T+0) ≤rk(T) +rk(o)

A: We are given that τ,σ∈L(V,W) We suppose, w∈Im(τ+σ)   ....(1) So, there exists some v∈V such that…

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: ● Let A = [0, 1) and B = [1,2] U [1,2], then (2 pts) Find sup (An B), sup (A), and sup B

A: Given that and Now, recall  the fact  the definition of Supremum.Let (1) (2) For any there exists  a…

Q: Evaluate S (vz +va) 1 dz avz.

A: We will solve the integration.

Q: Let Q be an m xn nauix with ni >n and orthanormal columms, then we have both Q' Q = 1, and QQT -1 O…

A: The solution of the problem is given in the next step.

Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: 2 16 v2 6. Prove that x V(2 – x) dr = 15

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

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Q: tr(AA') = (tr(A))* There exist square matrices A and B such that AB-BA=I.

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Q: Evaluate S (x-3y+z)ds 1 where S is z = 1, x² + y² ≤36.

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Q: 46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

A: We have to solve the given integration

Q: Show V(X)

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: se se fe and az ryz 1. Let f(x, y, z) then find the value of %3D x+y + z ax' dy

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Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,