Question: In a typical week a person takes the bus five times in the morning and three times in the evening. Suppose the waiting time for the bus in the morning has mean 3 minutes and variance 2 minutes2, while the waiting time in the evening has mean 6 minutes and variance 4 minutes2.
(a) Let Xi denote the waiting time in the ith morning of the week, i = 1, ... , 5, and let Yj denote the waiting time in the jth evening of the week. Express the total waiting time as a linear combination of these X's and Y's.
(b) Find the expected value and the variance of the total waiting time in a typical week. State any assumptions needed for the validity of your calculations.