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Question 1: The joint distribution of three continuous random variables X, Y, and Z is uniform over the cylinder R = {(x, y, z) : x² + y² ≤ 1, 0 < z < 4}. Recall that the volume of a cylinder is r²h, where r is the radius and h is the height. Determine the following. a. The joint probability density function of X, Y, and Z. b. P(X² + y² ≤ 0.5 and Z < 2). c. Marginal probability density function of X. d. Marginal probability density function of Z. e. Are X, Y, and Z independent?

Question 1: The joint distribution of three continuous random variables X, Y, and Z is uniform over the cylinder R = {(x, y, z) : x² + y² ≤ 1, 0 < z < 4}. Recall that the volume of a cylinder is r²h, where r is the radius and h is the height. Determine the following. a. The joint probability density function of X, Y, and Z. b. P(X² + y² ≤ 0.5 and Z < 2). c. Marginal probability density function of X. d. Marginal probability density function of Z. e. Are X, Y, and Z independent?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1: The joint distribution of three continuous random variables X, Y, and Z is uniform over the cylinder R = {(x, y, z) : x² + y² ≤ 1, 0 < z < 4}. Recall that the volume of a cylinder is r²h, where r is the radius and h is the height. Determine the following. a. The joint probability density function of X, Y, and Z. b. P(X² +Y² ≤ 0.5 and Z < 2). c. Marginal probability density function of X. d. Marginal probability density function of Z. e. Are X, Y, and Z independent?
Transcribed Image Text:Question 1: The joint distribution of three continuous random variables X, Y, and Z is uniform over the cylinder R = {(x, y, z) : x² + y² ≤ 1, 0 < z < 4}. Recall that the volume of a cylinder is r²h, where r is the radius and h is the height. Determine the following. a. The joint probability density function of X, Y, and Z. b. P(X² +Y² ≤ 0.5 and Z < 2). c. Marginal probability density function of X. d. Marginal probability density function of Z. e. Are X, Y, and Z independent?
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