Question

Let X be a random variable such that P(X<=0)=0 and let mu=E(X) exist. Show show that P(X>=2mu)<=1/2

Answer 1

An application of Markov's Inequality should do the trick:
\[P(X\ge a)\le\frac{E(X)}{a}\]
Just replace \(a\) with \(2\mu\).