A pharmaceutical company has developed a new drug that helps insomniacs sleep. In tests of the drug, it records the daily number of hours asleep and awake. Let X denote the number of hours awake and let Y denote the number of hours asleep for a typical patient.
(a) Explain why the company must model X and Y as dependent random variables.
(b) If the company considers the difference between the number of hours awake and the number asleep, how will the dependence affect the SD of this comparison?