An inspector selects an item for inspection according to the outcome of a coin flip: the item is inspected if the outcome is head. Suppose that the time between item arrivals is an exponential random variable with mean one. Assume the time to inspect an item is a constant value t.
(a) Find the PMF for the number of item arrivals between consecutive inspections.
(b) Find the PDF for the time X between consecutive inspections?
(c) Find the value of t, so that with a probability of 90% an inspection is completed before the next item is selected for inspection?