Problem 8. A certain part is loaded on a manufacturing machine for processing. The time to complete the processing is distributed exponentially with mean Up. A plant worker supervises the process. He performs checks on the part according to the Poisson process with parameter A. After any such check, he either removes the part from the machine (if the check reveals the part has been completed), or performs some tweak in the machine's setup (if the part has not been completed yet) and leaves. Assume that the checks and the tweaks are done instantaneously. a) After the part has been loaded on the machine to begin processing, how soon is it expected to be removed? b) How will your answer to Question (a) change if each tweak doubles the parameter of the exponential function for the time until process completion (originally, ,u)? (Provide an expression.)