The length of time that a machine operates without failure is denoted by Y1 and the
Chapter 6, Problem 6.98(choose chapter or problem)
The length of time that a machine operates without failure is denoted by Y1 and the length of time to repair a failure is denoted by Y2. After a repair is made, the machine is assumed to operate like a new machine. Y1 and Y2 are independent and each has the density function f (y) = $ ey , y > 0, 0, elsewhere. Find the probability density function for U = Y1/(Y1 + Y2), the proportion of time that the machine is in operation during any one operationrepair cycle.
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