Problem 4.17 Which of the following functions F(x) are continuous dfs of the form dis[1]played in Definition 4.1? Calculate the corresponding pdf f(x) where appropriate.

(a) F(x)=0, x ≤ 0, F(x) = x 1 + x ,x> 0;

(b) F(x)=0, x ≤ 2, F(x)=1 − 4 x2 ,x> 2;

(c) F(x)=0,x< −π/2, F(x) = sin x, −π/2 < x < π/2, F(x)=1, x ≥ π/2.