A professor receives phone calls at random times T(i). Let W(i)=T(i)-T(i-1) be the elapsed time between two consecutive phone call arrival times T(i-1) and T(i). The W(i) are independent, identically distributed random variables with density f(w)=5exp(-5w), w>0. Wi is measured in hours.
Assume that the professor is away from his office on a given day between 1:15pm and 1:45pm and between 4:45pm and 5:15pm. What is the probability that the professor does not miss any incoming phone calls during the time he is away from the office?