What’s the best way to estimate a product?

What’s the best way to estimate a product? Two survey analysts – for lack of my imagination just call them A and B – are having a dispute. They have conducted a survey aimed at estimating the amount of time students spend in-commute to and from the U. The survey is simple: A random sample of commuting students are asked (1) how many commutes to campus did you make last week, and (2) how many minutes, on average, is your commute? Analyst A proposes the following estimator: Calculate the average number of commutes, call it C, and

the average (of the average) time in minutes per commute, call it T, then mulitply: C×T. B proposes the alternative: First multiply each subject’s reported number of commutes and time per commute, then compute the average of these products. Who is right, which estimator is better? In what sense is that one better? Are there circumstances in which the estimators are equally good? Explain. Are these circumstances, if any, likely to hold here?