Suppose we choose a random point in the interval (-2, 1) and denote the distance to 0 by X. Prove that X is a continuous random variable.
If you begin with a random variable Y that is uniformly distributed on the interval (-2,1), then it is reasonable to think of Y as a randomly chosen point. Then by definition X=|Y|, Y’s distance from zero. Now one characterization of continuous random variable is: the range of the variable includes an interval of real numbers, bounded or unbounded. The range of X is [0,2).