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Math Help - Exponential distribution

  1. #1
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    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
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  2. #2
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    Re: Exponential distribution

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

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