A function g : R - R is said to be L-Lipschitz continuous for a given real number L 2 0 if Ig(x) - g(y)| 0. Fix 8 > 0. Prove that for any a E R we have [PIX E [a, a + 8] - 8fx(a)| 0 we have P[X E [a, a + 8]] ~ ofx (a). Explain what happens if fx (a) = 23.4