12. Let X be an RV of the continuous type, and let Y = g(X) be defined as follows:

(a) g(x) = 1 if x > 0, and = −1 if x ≤ 0.

(b) g(x) = b if x ≥

b, = x if |x| <

b, and = −b if x≤−b.

(c) g(x) = x if |x| ≥

b, and = 0 if |x| < b.

Find the distribution of Y in each case.