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Well the question is a little easier .. Let X be a random variable that follows a Uniform distribution (0,1)(Uniform Standard). What is rank of the variable? (Values ​​can take). I have a confusion between whether the variable can take real values ​​between the interval (0,1) or can only take the values ​​0 or 1

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Can you write the density function for $X$ uniformly distributed over $[0,1]$? Those points with non-zero probability belong to the rank of $X$! – user21436 Jan 24 '12 at 17:00
@Kanna: Be careful that here, every point has zero probability... I see what you mean to ask by your second question but it needs to be slightly reformulated. – Did Jan 24 '12 at 17:08
@DidierPiau Thank You very much! Sure, I meant "non-zero density"! – user21436 Jan 24 '12 at 17:35
@Kan: Yes. With the further caveat that the density function is only defined almost surely... Hence for every point there exists a density function which is zero at this point... :-) – Did Jan 24 '12 at 17:47

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Let X be a random variable that follows a Uniform distribution (0,1)(Uniform Standard).

Do you mean a discrete or a continuous distribution? Do you mean [0,1] or (0,1)? Or are these your questions?

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Sorry is a continuos distribution. that is X ~ Uniform (0,1). I thought that the random variable that follows a standard uniform distribution is understood to be a continuous distribution (by definition) – Melkhiah66 Jan 24 '12 at 23:10
Melkhiah: If the definition is well known to you, why do you ask this question? – Did Jan 26 '12 at 6:57

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