Suppose your waiting time for a bus in the morning is uni- formly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.

a. If you take the bus each morning and evening for a week. what is your total expected waiting time? [Hint: Define rv's X, X and use a rule of expected value.]

b. What is the variance of your total waiting time?

c. What are the expected value and variance of the differ- ence between morning and evening waiting times on a given day?

d. What are the expected value and variance of the differ- ence between total morning waiting time and total evening waiting time for a particular week?