If X(1), X(2), ..., X(n) are independent and identically Exponential distribution with mean u,
Show, by using the Chebychev's inequality, that X(n)/n converges to zero in probability.
P(|X-E(X)|>c)<Var(x)/c^2 for any c>0.
I only managed to use the inequality to prove that X(n)/n converges to u/n where u is the mean.
But any idea how to get rid of the n at the denominator? I am supposed to prove that it converges to zero.
Really appreciate if anyone can help :)