Buses run every 15 minutes along a certain route during rush hour. The time that a person would have to wait at a bus stop is uniformly distributed between 0 and 15 minutes.
- What is the probability that this person has to wait between 5 and 10 minutes for the next bus?
- What is the probability of a wait of at least 12 minutes?
- Determine the expected waiting time and variance of waiting times.