One day at noon, you have a sudden craving for a California burrito from the Taco Stand, and you decide to take the bus from campus into town. Starting at noon, suppose that the number of minutes until the first bus arrives is an exponential random variable with parameter 1/20

(a) If you have already been waiting for 10 minutes (i.e. it is 12:10 pm) and the first bus has not yet come, what is the probability that you will have to wait at least 15 additional minutes?

(b) Repeat part (a) under the assumption that the number of minutes from noon until the first bus is uniformly distributed over [0,40].

(c) Explain how the answers to (a) and (b) relate to whether exponential and uniform random variables are memoryless