19. If the distribution function of X is given by

$$

F

(b) = \begin{cases}

0 & b < 0 \\

\frac{1}{2} & 0 \le b < 1 \\

\frac{3}{4} & 1 \le b < 2 \\

\frac{7}{8} & 2 \le b < 3 \\

\frac{15}{16} & 3 \le b < 3.5 \\

1 & b \ge 3.5

\end{cases}

$$

calculate the probability mass function of X.