# Math Help - Exponential distribution

1. ## Exponential distribution

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.

Chebychev's inequality:

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

2. ## Re: Exponential distribution

This problem has got to mean converges as $n \to \infty$

If that's the case then clearly $\displaystyle \lim_{n \to \infty} \frac{u}{n} = 0$