2. Suppose that you are waiting for a friend to call you andthat the time you wait in minutes has an exponential distributionwith parameter λ = 0.1. (a) What is the expectation of your waitingtime? (b) What is the probability that you will wait longer than 10minutes? (c) What is the probability that you will wait less than 5minutes? (d) Suppose that after 5 minutes you are still waiting forthe call. What is the distribution of your additional waiting time?In this case, what is the probability that your total waiting timeis longer than 15 minutes? (e) Suppose now that the time you waitin minutes for the call has a U(0, 20) distribution. What is theexpectation of your waiting time? If after 5 minutes you are stillwaiting for the call, what is the distribution of your additionalwaiting time?
3. The arrival times of workers at a factory first-aid roomsatisfy a Poisson process with an average of 1.8 per hour. (a) Whatis the value of the parameter λ of the Poisson process? (b) What isthe expectation of the time between two arrivals at the first-aidroom? (c) What is the probability that there is at least 1 hourbetween two arrivals at the firstaid room? (d) What is thedistribution of the number of workers visiting the first-aid roomduring a 4-hour period? (e) What is the probability that at leastfour workers visit the first-aid room during a 4- hour period?
