Suppose that a point (X,Y) is chosen at random from the region S on the xy-plane containing all points (x,y) such that x>= 0; y>= 0, and 6y+x<= 3. (a) Determine the joint p.d.f. of X and Y: (b) What is P(Y=X)? (c) What is P(X>=1)?

Q: 2. Generate 10 normally distributed random points in 3-D space, and join them with lines in one 3-D…

A: [X,Y] = meshgrid(0:.25:5,0:.25:5); Z = sqrt(X.^2 + Y.^2); figure(2) mesh(X,Y,Z) title('surface z =…

Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

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A: Given,

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Q: (b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤…

A: As according to the guidlines we can solve only one question please post the other question…

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A: as per our guidelines we are supposed to answer only one question. Kindly re post other question as…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (4,0,0), (0,3,0), and (0,0,2)

A: we have to find triple integral

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A: We will find range for x,y and z and then triple integral

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Q: Let R be the region in the half plane x 20 bounded by the curves y = -5x + 5 y = x2 – 1 x = 0…

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Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: 2. 7 3. Find the centroid of the region bounded by y 3, 3 to the nearest thousandth. nd Since you…

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A: We have to find the volume integral of the given function.