Mass, Moments, and Probability Density Functions Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the centroid for a lamina with over the region bounded by the curve and the line in the first octant.

(2) Find the centroid for a lamina with over the region between the line and the parabola

(3) Find the centroid for the part of the spherical solid with density described by and

(4) Find the centroid for the solid bounded by the surface and where the density is

(5) Use double integration to find the center of mass of a lamina covering the region with density function

(6) Use double integration to find the center of mass of a lamina covering the region bounded by and with density function

(7) Use double integration to find the center of mass of a lamina covering the region bounded by and with density function

(8) A lamina has the shape of a semicircular region Find the center of mass of the lamina if the density at each point is directly proportional to the square of the distance from the point to the origin.

(9) Find the center of mass of the cardioid if the density at each point is

(10) Find the centroid of the loop of the lemniscate that lies in the first quadrant.

(11) Find the centroid of the part of the large loop of the limacon that does not include the small loop.

(12) Find the center of mass of the lamina that covers the triangular region with vertices if and are both positive and the density at is directly proportional to the distance of from the -axis.

(13) Suppose the joint probability density function for the random variables and is



Find the probability that

(14) Suppose the joint probability density function for the random variables and is



Find the probability that

(15) Suppose the joint probability density function for the random variables and is



Find the probability that

(16) Suppose the joint probability density function for the random variables and is



Find the probability that

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Cite this as:
Mass Moments And Probability Density Functions Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/mass-moments-and-probability-density-functions-homework.html