The total time X (in minutes) from the time a supercomputer job is submitted until its run is completed and the time Y the job waits in the job queue before being run have the joint density function

The CPU time for the job (i.e., the length of time the job is in control of the supercomputer’s central processing unit) is given by the difference W = X - Y. Find the density function of a job’s CPU time. You may use the facts that

and ∫ ye^-y dy = -ye^-y + ∫ e^-y dy in determining the density function.

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