What are the potential distributions for a continuous variable X on [0, 1], if |2X - 1| is known to have a uniform distribution on [0, 1]? Will the distribution of INT(2X) always be uniform on {0, 1} ?
This question arises in a potential proof that the digits of the number Pi in base 2 (see exercise 7 in this article), distributed as INT(2X) and obviously being equal to 0 or 1, are uniformly dist…