Solved – Does uniform distribution belong to location and scale family?

For any given distribution (on $mathbb{R}$, say, or an interval) $f_0$, we can generate a location-scale family by $$ f(x ; mu,sigma) =frac1{sigma} f(frac{x-mu}{sigma}) $$ The distribution family most often considered with the uniform distribution is $U(0, theta), theta > 0$ which is a one-parameter family and so cannot be written in location-scale form. If you with your question consider the family $U(a,b),a<b$ where $a,b$ otherwise are free, then you can write that in scale-location form. You can for example chose for $f_0$ $$ f_0(x)= frac12, quad -1 le x le 1 $$