In: Statistics and Probability
A group of n people get on an elevator at Floor 0. There are m floors besides Floor 0. Each person uniformly randomly chooses one of those m floors to stop at. (All choices are independent, and no one gets on the elevator after Floor 0.) The elevator stops at a floor if at least one person has chosen to stop there. Let X be the number of stops that the elevator makes after Floor 0.
(a) What is E[X]? Var(X)?