3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1, Cov(X, X2) 0, and Cov(Y, Y2) 0.5

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Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

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Q: Show that o (z) = x² – x=1 is an implicit solution to z² = 2y on the interval (0, 0). %3D %3D

A: Here, the given equation is: x2d2ydx2=2y...(1) To show that ϕ(x)=x2-x-1 is the solution of (1) on…

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A: To evaluate: The integral of . Formula used: Integration Formula:

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A: We have to prove given identity: Concept:

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: 1. Suppose that Var(X) = 3, Var(Y ) = 4, and Cov(X, Y ) = 1. (a) Find Cov(2X − Y, X + 3Y ). (b) Find…

A: Given, Var(X) = 3, Var(Y ) = 4, and Cov(X, Y ) = 1       To find, a) Find Cov(2X − Y, X + 3Y ).b)…

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Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: 2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

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Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

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Q: hat polynomial x^2 + y^2 + y^2 − xy − yz − zx is irred

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Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

A:

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: 4. Prove that: Jx'J,Ex) dx 2 3x J,Cx)-(x-3x) J.cx) -3

A: We find the value of the integration by apply the integration by parts and the recurrence relation.…

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Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

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Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

A:

Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

A: Compute the marginal density function of y1 using the formula: fy1=∫y2fy1,y2dy2 fy1=∫014y1y2dy2…

Q: 5. Knowing that (2" J,(x))' = x" J,-1(x) (x-" J,(x))' = -x=" Jp+1(x) 2v Jy-1(x) + Jp+1(x) = Jy-1(x)…

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Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

A:

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A: ddxsinnx =cosnxddxnx =ncosnx

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Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: 2 2. Evaluate the iterated integral 6x'y dady

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Q: Estimate x using the trapezoid rule withn=4 a. Type equation here. Redo 9 using Simpson's rule. a.…

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A: How to find the sufficient statistic 1. Find the likelihood function 2. Apply the Neymann…

Q: that X and Y have joint pdf f(x, y) ={x + 3x^2y if 0 <= x <= 1 and 0 <= y <= 1, 0 otherwise.   (c)…

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Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

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Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…