1. X and Y have following joint PDF S2, x+ ys 1;x2 0; y 2 0 10, fxx (x, y) = %3D otherwise a. Find the marginal PDF of X. b. Find the marginal PDF of Y. c. Find Cov[X,Y]. d. Are X and Y independent? Justify your answer.

Q: Exercise 2. Integrate the following functions. 1. S(3x+2)°dz 2. 3.

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A: We know that, ddx1x=-1x2 Also, ddxaf(x)=addx(f(x)) where a is a constant.

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A: Here, the two chord are congruent. So, the corresponding arcs are also congruent.

Q: find dy if y

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A: In the separation of variables method of solving the differential equation, the different variables…

Q: ots.) Let f (x) = and g(x)= 2x+3. X-3 %3D a. Find (fog)(x) b. Find (gof)(x) C. Are f and g inverse…

A: a) Plug g(x)=2x+3 inside f(x) and then simplify.

Q: Let X and Y have the joint PDF f(x,y) = 2e−x−y for 0<x<y<∞. Find the joint PDF of Z = 2X and W = Y −…

A: f(x,y)°2e−x−y ; 0&lt;x&lt;y&lt; ∞

Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

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Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

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Q: What is the rule used to transform ΔABC to its image?A(−3, 5), B(2, 8), C(−4, −5) and A'(−3, −5),…

A: The objective of the question is to identify the transformation rule that was used to transform…

Q: 23. z = y4 - 2y² + x² 17 16

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