What is the mean and variance if you roll the die n times?

Ottawa's Confederation Line trains arrive at peak times at a station
to a station on a Poisson basis, averaging 10 trains per hour.
1. What is the waiting time distribution of three trains? What is the
What is the probability that this waiting time is at most 25 minutes? What
What are the mean and variance of this random variable?
2. No train arrives during the first 5 minutes of waiting. What is the
What is the probability that there will be no train during the next 3 minutes?
3. What is the probability that two trains will arrive in twelve minutes?
4. At 95%, at least one train arrives in t-minutes. What is approximately
t in minutes?
5. A period of 5 minutes is said to be empty if it contains no arriving
of trains. What is the probability that at most one 5-minute period
is empty in one hour?