Suppose that P(X = 1) = P(X = -1) = 1/2, that Y ∈ U(-1, 1) and that X and Y are independent.
(a) Show, by direct computation, that X + Y ∈ U(-2, 2).
(b) Translate the result to a statement about characteristic functions.
(c) Which well-known trigonometric formula did you discover?