The durations of calls to a radio talk show are known to be exponentially distributed with a mean of 3 minutes.
a. What is the probability that a call will last less than 2 minutes?
b. What is the probability that a call will last longer than 4 minutes?
c. Given that a call has already lasted 4 minutes, what is the probability that it will last at least another 4 minutes?
d. Given that a call has already lasted 4 minutes, what is the expected remaining time until it ends?