The city bus outside Weil Hall is never on time; it is either three minutes early (-3), one minute early (-1), one minute late (+1) or three minutes late (+3). The bus is 3 minutes late twice as often as it is 1 minute late. It is equally likely to be 3 minutes early as it is to be 3 minutes late and equally likely to be 1 minute early as it is to be 1 minute late. Assign a random variable B to denote the number of minutes the bus is off schedule.
1. Give the pmf of B.
2. If you make it to the bus stop 2 minutes before it is scheduled to arrive, what is the probability you catch the bus?
3. Given that you got to the bus 2 minutes before schedule and it has not arrived, what is the probability the bus is one minute late?
4. What is the variance of B?