Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 36 / 3 / b / ii / Solution

When $\mu =\mathbb{E}X>0$, the event $X=0$ implies $|X-\mu |\ge \mu$. The Chebyshev inequality therefore givesThis is the second moment method for proving that a nonnegative count is positive.