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 0

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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
S(x, y)= {C(r² + y? )
Sc+y²
0 <x, y < 1
otherwise
•Find the value of the constant C.
•What is the probability that both machines are in operation for more
than half an hour?
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 S(x, y)= {C(r² + y? ) Sc+y² 0 <x, y < 1 otherwise •Find the value of the constant C. •What is the probability that both machines are in operation for more than half an hour?
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