If X is uniformly distributed over a b what random variable

If X is uniformly distributed over (a, b), what random
variable, having a linear relation with X, is
uniformly distributed over (0, 1)?

Solution

The random variable X-a is uniforly divided over (0,b-a). Now, divide it by b-a.

Thus, the new variable Y=X/(b-a)-a/(b-a) is uniformly distributed over (0,1).