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

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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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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?