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Math Help - random variable explanation

  1. #1
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    random variable explanation

    Can someone explain these statement?

    "For any random variable X and \varepsilon >0, there is N such that  P(|X|> \varepsilon \cdot N) < \varepsilon."

    I am learning probability for first time and now learning random variable and distribution function. For these statement I am wanting to know how this relates to distribution function of X.
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  2. #2
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    Is this other form of Markov inequality?
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  3. #3
    MHF Contributor matheagle's Avatar
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    Divide by N and think as epsilon as a VERY small real number...

     P\left({|X|\over N}> \varepsilon \right) < \varepsilon

    They're saying that the probability of  {|X|\over N} being bigger than zero is very small.

    In other words...  {|X|\over N}\to 0
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