Timothy decides to work out and goes for a 6 mile bicycle ride. But Timothy isn't very fit, so he will have to stop every now and then to take a breather. His breaks will vary depending quickly he catches his breath. Let us model the number of breaks Timothy has during one of his 6 mile rides with a random variable X that has a Poisson distribution of = 1. Bob, Timothy's brother, who is also quite unfit, also rides the same path, and also stops when he is tired. The duration of his stops is modeled with a random variable Y with a mean of 0.9 minutes and variance of 1. The amount of times Bob pauses his ride for a breather is also a Poisson random variable X of = 1 and is independent of the length of the stops. If Bob doesn't take any pauses in his ride, he will travel 6 miles within 45 minutes.

1. If Bob stops 3 times for a breather, compute the expected length of Bob's ride by conditioning.
2. Again, if Bob stops 3 times for a breather, compute the variance of the length of Bob's ride by conditioning.
3. Compute the expected length of one of Bob's runs, including stops. You should approach this by conditioning on random variable X.