# random variable explanation

• Mar 9th 2010, 09:58 AM
memory loss
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.
• Mar 9th 2010, 12:39 PM
memory loss
Is this other form of Markov inequality?
• Mar 14th 2010, 11:15 PM
matheagle
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... ${|X|\over N}\to 0$