# Rank of a random variable that follows a Uniform Distribution (0,1)

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

• 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, 2012 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, 2012 at 17:08
• @DidierPiau Thank You very much! Sure, I meant "non-zero density"!
– user21436
Jan 24, 2012 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, 2012 at 17:47

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?

• 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) Jan 24, 2012 at 23:10
• Melkhiah: If the definition is well known to you, why do you ask this question?
– Did
Jan 26, 2012 at 6:57