Suppose your waiting time in minutes for the bus in the morning is uniformly distributed on [0, 5], whereas waiting time in the evening is uniformly distributed on [0, 10]. Each waiting time is independent of all other waiting times.

(a) If you take the bus each morning and each evening for 5 days in a row, what is your total expected waiting time?

(b) What is the variance of your total waiting time?

(c) What is the expected value of the difference between the total evening waiting time and the total morning waiting time over all 5 days?

(d) What is the variance of the difference between the total evening waiting time and the total morning waiting time over all 5 days?

Explain each step in detail.