# Homework Help: A question about uniform distributions

1. Dec 8, 2012

### 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?

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.