A certain pool is staffed by unreliable lifeguards. The lifeguards are numbered 1 through n and they all start on duty at the same time every day. The pool remains open as long as at least two of the lifeguards are on duty. Suppose that, on any day, independently of the others, lifeguard i stops working at a time which is a random variable with distribution function Fᵢ. In terms of the Fᵢ's, find the survival function of the period that the pool stays open.

Question

Quizplus · Accepted Answer

The Answer of A certain pool is staffed by unreliable lifeguards. The lifeguards are numbered 1 through n and they all start on duty at the same time every day. The pool remains open as long as at least two of the lifeguards are on duty. Suppose that, on any day, independently of the others, lifeguard i stops working at a time which is a random variable with distribution function Fᵢ. In terms of the Fᵢ's, find the survival function of the period that the pool stays open.

A Certain Pool Is Staffed by Unreliable Lifeguards