A question about uniform distributions

[Artusartos]

If we have a uniform distribution on [0,x]...then the pdf is 1/x right? But what if we have [0,x)? Do we still have the same pdf?

Thanks in advance.

 

[Mute]

Since x is usually used as a variable, it would be better to write your pdf as being uniform on [0,a], and so the pdf is $\rho_X(x) = 1/a$. There is effectively no difference if you take the support of the pdf to be [0,a), as you have only removed a single point from the distribution, and the probability of measuring that point is zero in both cases. I suppose there is a slight technical difference in that in practice if the support is [0,a] it is possible that the result of a measurement would be exactly a, whereas for [0,a) it is impossible, but the pdf's are still the same.

(Even though the probability of drawing any specific number is zero, when you draw from a continuous probability distribution you always get some number, so even if something technically has zero probability of occurring, you can still draw it if it is in the support of the pdf.)