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Customers arrive according to a Poisson process of rate λ per hour. Joe does not want to stay…

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Customers arrive according to a Poisson process of rate λ per hour. Joe does not want to stay until the store closes at T – D 10 p.m., so he decides to close up when the first customer after time T – s arrives. He wants to leave early but he does not want to lose any business so he is happy if he leaves before T and no one arrives after. (a) What is the probability he achieves his goal? (b) What is the optimal value of s and the corresponding success probability?