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3. A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by f(x,y) = {9rye-(x+3y) x >0 and y > 0 otherwise a. What is the probability that both machines are in operation for more than an hour? b. Find the marginal probability density functions fx(x) and fy(y). c. Are X and Y independent? Explain.

3. A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by f(x,y) = {9rye-(x+3y) x >0 and y > 0 otherwise a. What is the probability that both machines are in operation for more than an hour? b. Find the marginal probability density functions fx(x) and fy(y). c. Are X and Y independent? Explain.

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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3. A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by [9xye-(x+3y) x>0 and y > 0 f (x,y) = {} otherwise a. What is the probability that both machines are in operation for more than an hour? b. Find the marginal probability density functions fx(x) and fy (y). c. Are X and Y independent? Explain.
Transcribed Image Text:3. A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by [9xye-(x+3y) x>0 and y > 0 f (x,y) = {} otherwise a. What is the probability that both machines are in operation for more than an hour? b. Find the marginal probability density functions fx(x) and fy (y). c. Are X and Y independent? Explain.
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