The absent-minded professor and the tardy student. A professor (absent-mindedby convention) gives each of two students an appointment at 12 noon. One ofthe students arrives on time; the second arrives5minutes late. The amount oftime the first student spends closeted with the professor isX1; the second studentengages the professor as soon as he is free and spends timeX2in conference withhim. SupposeX1andX2are independent random variables with the commonexponential distribution of mean30minutes. What is the expected duration fromthe arrival of the first student to the departure of the second