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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 (* + y?) 0

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 (* + y?) 0

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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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 (* + y?) 0 <x < 1 and 0 < y < 1 f(x) = otherwise What is the probability that both machines are in operation for more than half an hour? a. Find the marginal probability density functions fx(x) and fy(y). b. Are X and Y independent? Explain. c.
Transcribed Image Text: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 (* + y?) 0 <x < 1 and 0 < y < 1 f(x) = otherwise What is the probability that both machines are in operation for more than half an hour? a. Find the marginal probability density functions fx(x) and fy(y). b. Are X and Y independent? Explain. c.
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