Problem 1 The random variable X is uniform in the interval (-27, 27). Find fy (y) it (a) Y = X3 %3D (b) Y = X4 %3D (c) Y = 2 sin (3X +40°) %3D

Q: Find d²y dy if x = if x dx² 4(ln 6)² (62t+1) = e³t and y = 6²t+1

A: Given,

Q: According to a recent survey, 77% of husband-wife families with kids under 18 years old have life…

A: Let  n be the sample size  p be the probability of husband-wife families with kids under 18 years…

Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

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Q: QUESTION 5 (3 points) Find dy/dt. y= cos(/10+12) 5 -sin 10+12 5 sin(10t+12) 10t+12 1 sin(10t+12)…

A: Kindly see attached photo for your guidance.

Q: If f (8) = 40-2 then find f'(0) sin(x0)'

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Q: 2x3-4x-8 dx (x2-x)(x²+4)

A: Given ∫2x3-4x-8x2-xx2+4dx=∫2x3-4x-8xx-1x2+4dx..........(1) We shall use the Partial fraction method…

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Q: Question 5. Apply Laplace Transform to solve the following Differential Equation when x(0) = x'(0) =…

A:

Q: #23) y'(x) = 4 tan 2x-3 los x Saj (x) dx = S 4 tom 2x - 3 los x dx 3(x) = 4 S sin 2x dx - S3 losx.…

A: Here your answer is,-2lncos2x-3sinx+Cand the answer given in the book is,2lnsec2x-3sinx+C Here both…

Q: Problem 8. Use Problem 4 to prove that T(1/2) = /T by computing the explicit density of Z².

A: It is given that Z2 ~ Gamma (½, ½), if Z ~ N (0,1).

Q: y== Cosinlrx) a Ca Cosla.) aSatustied if x=

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Q: - sin ( 7u) If q(u) 3 + s°ds then | - (n),b q'(u)

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Q: 3, Let f (x) = Vx – 7. Find f 1 Of ' (z) = - Of'(z) = -V – 7 %3D 1 Of (x) = a° + 7 Of (x) = (x + 7)³…

A:

Q: (D-9)y 3e" +x-sin 4x. 3 1 A. y C,e*+C,e* +e* +÷x- sin 4x 25 -3x 8 3 1 B. y Ce* +C,e-* +e* -x- sin 4x…

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