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

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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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