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  denote the number of hours awake and...

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
 denote the number of hours awake and let
 denote the number of hours asleep for a typical patient.

(a) Explain why the company must model
 and
 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?