4. Suppose your waiting time (in minutes) X for a bus in the morning is uniformly dis- tributed on (0, 8), whereas waiting time Y in the evening is uniformly distributed on (U, 10), independent of morning waiting time. Additionally, you may assume that wait- ing times are independent on a day-to-day basis. a. If you take the bus each morning and evening during a ve-day work week, what is your total expected waiting time? b. What is the variance of your total waiting time? c. What are the expected value and variance of the difference between morning waiting time and evening waiting time on a given day? d. What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for the entire ve-day work week? 6. Suppose, in problem 4, that each morning's waiting time X is still uniformly distributed on (0, 8), but the ensuing evening waiting time Y, conditioned upon X = x, has the probability density function fy (y [ X = x) = exp{ }, y>0 y 50. Repeat parts a.-d. of the previous problem with these modified assumptions. (Ignore the possibility that the evening bus arrives after next morning's). Hint: Use the result of the previous problem to compute the first two moments of Y