I want to know whether any uniform distributed random variable is symmetric on any interval [a,b]. My thinking is it is symmetric on any interval [a,b]. i tried to think about a counter-example. But I didn't find any. Is there any?
I want to know this as I want to relate the uniform distribution to the location family, so that I can calculate ancillary statistics. Because if uniform distribution is symmetric on any interval, then the statistics based on order statistics are always ancillary.