9. A random variable X is called symmetric about 0 if for all x ∈ R,

Prove that if X is symmetric about 0, then for all t > 0 its distribution function F satisfies the following relations:

(a) P ????
|X| ≤ t
= 2F(t) − 1.

(b) P ????
|X| > t
= 2
1 − F(t)
.

(c) P(X = t) = F(t) + F(−t) − 1.

P(X) = P(X -x).